'//f^'y. 













Book_LB_2 



/ 

A TREATISE ON 



LOGIC, Y7f£ 



OR, 



TUE LAWS OF PURE THOUGUT; 



COMFBISIMO BOTH 



THE ARISTOTELIC AND HAMILTONIAN 
ANALYSES OF LOGICAL FORMS, 



AND 60ME CHAPTERS OF 



APPLIED LOGIC, 



By FRANCIS BOWEN, 

ALFORO PROFESSOR OF MORAL PHILOSOPHY IN HARVARD COLLEGE. 



" Nam neque decipitur ratio, nee decipit un((U!im." 

&Ianili[js. 



CAMBRIDGE: 
SEVEIl AND FRANCIS, 

BOOKSELLERS TO THE UNI VER^SITV. 

18 6 5. 



^ 






Entered according to Act of Congress, in the year 1864, by 

SEVER AND FRANCIS, 

In the Clerk's Office of the District Court of the District cf Maesaehnsetta. 



THIRD EDITION 



University Press* 

Welch, Big blow, and Company, 

Cambridge. 



PREFACE. 



THE revival of the study of Logic, at least in 
England and America, as an important ele- 
ment of a University education, dates only from the 
publication of Dr. Whately's treatise on the subject, 
little over thirty years ago. Yet so much has been 
accomplished for the advancement of the science 
during this short period, that this treatise, with all 
its excellences, must be admitted to be now as far 
behind the times as were the compilation by Al- 
drich, and the meagre compendium by Dr. Watts, 
the use of which it superseded. Dr. Whately lived 
long enough to be able to appropriate to himself 
the epigrammatic boast, that he had labored so ef- 
fectually as to render his own work useless. With- 
out the interest which was awakened in the study 
of the science by the publication of his book and 
the discussions which it excited, it is not too much 
to say that many of the valuable works upon Logic, 
which have appeared during the last thirty years, 
either would not have been written, or would have 
lacked some of their most interesting and impor- 
tant features. Sir William Hamilton's own labors 
in this department, by which he certainly accom- 
plished more for the science than has been done by 
any one man since Aristotle, began with an elabo- 



IV PREFACE. 

rate article on Dr. Whately's treatise in the Edin- 
burg Review, a paper which, as he has himself 
declared, contains the germs of all his subsequent 
discoveries. Besides what Hamilton has accom- 
plished, the publications within this period of Pro- 
fessor Mansel, Dr. Thomson, Mr. De Morgan, Mr. 
Boole, Mr. J. S. Mill, and a host of others, have 
given an entirely new aspect to the science. Among 
recent American works upon Logic, honorable men- 
tion ought to be made of those bj Mr. Tappan, and 
bj Dr. W. D. Wilson of Geneva. 

The only hope that this volume may be found 
to be of some use consists in the fact, that, as I was 
the last to enter the field, I have been able to profit 
by the labors of my predecessors. Certainly it 
could not have been written without their aid, and 
one of the chief objects held in view in the prepa- 
ration of it has been to gather together, and digest 
into system, their several improvements and eluci- 
dations of the science. At the same time, the 
work would not have been carried on in the same 
spirit in which they began it, if I had not ventured 
respectfully to dissent from some of their doctrines, 
and even to present some opinions which will very 
likely be found to have no other merit than that 
of originality. As Le Clerc remarks, in introducing 
his own lucid and thoughtful compendium of the 
science to the reader's notice, "5t, in hacce Logica, 
nihil esse novi, aut pleraque 7iova dixerim, lector em perinde 
fcfelleroy 

When Dr. Whately wrote, it was not so frequent 
a practice as it has since become for English schol- 
ars to profit by the labors of their German breth- 
ren, and hence some of the greatest deficiencies 
of his book. It cannot be said that the study of 
Lps^ic ever declined in the schools of Germany, as 



PREFACE. 



it did in those of France, England, and this country. 
Upheld for a time by the genius of Leibnitz and 
the indefatigable industry of Wolff, it was at last 
reduced to rigorous system, its boundaries were 
fixed, and its relations to Psychology and Metaphys- 
ics accurately determined, by the master mind of 
Kant. Though this great Metaphysician prepared 
no distinct work upon the subject, the volume re- 
lating to it which passes under his name being a 
mere compilation from his loose notes by Jasche, 
the science has profited more by his labors than by 
those of any other Continental writer of modern 
times. Indeed, the publication of his " Criticism of 
Pure Eeason" formed hardly less an era in the his- 
tory of Logic than in that of Metaphysics. In one 
respect, it is true, it had an injurious influence, as 
it established the practice, which has since become 
wellnigh universal in Germany, of modifying the 
doctrines of this science in order to furnish a basis 
on which might be erected any peculiar scheme 
of speculative Philosophy. Since Kant's time, a 
multitude of treatises upon Logic have been pub- 
lished by German writers, about half of them hav- 
ing no other purpose than that of preparing the 
way, and furnishing the materials, for some extrav- 
agant speculations in Metaphysics. This mode of 
treatment was carried to an outrageous extent by 
Hegel, who labored to break down altogether the 
boundary that had been established by Kant, and 
whose elaborate work, bearing the name of Logic, 
is a mere perversion and caricature of that science, 
as it is metaphysical from beginning to end. Even 
Trendelenburg, who has contributed more than 
any other person to the rapid decline of Hegel- 
ianism in Germany, is not free from blame in this 
respect, his very able work, Logischc TJiitermchimgeny 



VI PREFACE. 

being devoted in great part to building up a phil- 
osophical system of his own. 

But the very prevalence of this abuse in Ger- 
many furnishes an additional motive for the study 
of the subject. A key to German Metaphysics 
can be obtained only by a thorough mastery of 
the principles and the terminology of Logic. To 
some persons, perhaps, this consideration may not 
have much weight, as they will object, that it is 
of little use to be able to open the door, if the 
room contains little more than rubbish. Still I 
cannot but believe — and the opinion is founded 
on considerable experience as an instructor in 
both departments — that a fair knowledge of Log- 
ic is a natural, and even an indispensable, prepara- 
tion for the successful pursuit of Psychology and 
Metaphysics; — may I not add, of any philosoph- 
ical speculations whatever? It appears certain, 
that the University lectures of Kant, Fichte, Schel- 
ling, and Hegel could not have been made even 
intelligible, much less instructive, to hearers who 
had not previously acquired at least the elements 
of Losrical science. Hence the multitude of man- 
uals and text>books upon this subject, which have 
appeared in Germany during the last three quar- 
ters of a century, many of them having passed 
through numerous editions, and each betraying 
very plainly the particular system of Philosophy 
to which it was intended to serve as an introduc- 
tion. Some familiarity with the principles of Log- 
ic appears essential for a thorough comprehension 
even of the metaphysical doctrines of Sir William 
Hamilton, which, both in their philosophical and 
theological bearings, seem likely to exert a consid- 
erable influence over English and American minds 
for many years to come. 



PREFACE. VU 

Hamilton's "Lectures on Logic" are marked 
with the inevitable defects of a posthumous pub- 
lication, the larger portion of which was probably 
never intended by the author to be given to the 
public ; and though very ably edited by Professor 
Mansel and Mr. Veitch, they present a mass of 
crude material from which a knowledge of the 
peculiar doctrines of the writer cannot be ex- 
tracted but with considerable difficulty. Indeed, 
the " Lectures," which form the body of the book, 
were evidently prepared in great haste, when the 
author's appointment to the Professorship in this 
department, in 1836, obliged him to collect at 
short notice the materials for an extended course 
of instruction. He appears to have met this sud- 
den call by hurriedly translating a series of ex- 
tracts from the most approved German text-books, 
especially those of Krug, Esser, and Bachmann, 
merely interpolating here and there some of the 
comments, corrections, and additions which could 
not fail to occur to so rich a mind as his, while 
traversing so broad and familiar a field. These 
Lectures, containing only a glimpse of one feature 
of the peculiar system which has since become 
identified with his name, he seems to have re- 
peated from year to year, during his whole period 
of office, with no material enlargement or altera- 
tion of the manuscript, though doubtless inserting, 
from year to year, many extemporaneous exposi- 
tions of his corrections of the leading doctrines 
of Logical science, as these occurred to him at suc- 
cessive periods. The whole transaction seems to 
me to affi)rd an instructive comment on the futility 
of what is called the Professorial mode of teaching, 
which has always prevailed in the University of 
Edinburgh, and which consists in getting up very 



Vlll PREFACE. 



hastily a course of lectures during the teacher's 
first year of office, and repeating them, parroWike, 
from year to year, without any regular use of a 
text-book or manual of instruction. If such lec- 
tures contain anything really valuable, in addition 
to what is already before the world, they are apt 
very soon to find their way to the press ; if they 
are 'of little worth, they are almost sure to be 
repeated, with little alteration, to one class after 
another, and with as little profit to the hearer as 
exercise to the reader. It may be doubted wheth- 
er the most fertile and best-trained minds, at least 
in the speculative sciences, are capable of prepar- 
ing every year an entirely new course of lectures, 
without either filling them with crudities and tru- 
isms, or lapsing into paradox and extravagance, 
such as have too frequently characterized the pro- 
ductions of German Professors. 

With all his amazing activity of mind and pro- 
digious erudition, Hamilton appears to have been 
either too indolent, or too critical of his own labors, 
to be able, without great delays, to digest his mate- 
rials into a shape fit for publication. He was not 
an adept in the very low, but very necessary, art 
of book-making. But for his controversy with Mr. 
De Morgan, I doubt whether he would ever have 
worked up into form as much as he did of his 
" New Analytic of Logical Forms," the publication 
of which was promised as far back as 1846. Stim- 
ulated by opposition, however, though impeded 
by ill-health during the later years of his life, he 
appears to have labored strenuously, after the last- 
mentioned date, to fulfil this promise. Death sur- 
prised him long before he had completed his prep- 
arations ; and out of the mass of fragmentary ma- 
terials which were found among his papers, with 



PREFACE. UC 

some aid from the few critical and controversial 
articles that he had already printed, his editors 
pieced together, with great difficulty, the imperfect 
view of his improved system of Logic, which ap- 
pears as a long Appendix to the volume of his 
Lectures. The manuscripts which they selected 
and arranged were judiciously printed just as he 
left them, and with very little editorial comment. 
The reader must gather from them as best he 
may, always keeping in view the date attached 
to each fragment, a connected view of Sir William 
Hamilton's latest doctrines upon the subject. This 
posthumous work has at least one odd character- 
istic, as the body of the work and the Appendix 
flatly contradict each other, by giving opposite 
views of the science to which they relate. 

These are the sources whence I have endeav- 
ored to collect the materials for a general survey 
of the science of Logic in its present state, em- 
bracing what is common to all systems, and a re- 
view of most of the questions relating to it which 
are still open to discussion. Among English au- 
thors, after Sir William Hamilton, I have been 
chiefly indebted to Professor Mansel ; for without 
the aid afforded by his Prolegomena Logica, and the 
notes and supplementary matter appended to his 
edition of Aldrich, of which Hamilton justly re- 
marks that la sauce vaut mieux que le poisson, this 
book would have cost me much more labor, and 
yet would have wanted what are now its best 
claims to notice. I have also derived much help 
from the excellent " Outline of the Laws of 
Thought," by Dr. Thomson, the present Arch- 
bishop of York. Among the German writers, be- 
sides all whose names have been already men- 
tioned, I have made profitable use of Kiesewetter, 



X PREFACE. 

Fries, Beneke, Dressier, and Drobisch, besides con- 
sulting a host of others. Of the earlier logicians, 
it seems to me that Burgersdyck, with the anno- 
tations of Heereboord, gives the clearest account 
of the science as it was taught in the schools be- 
fore the influence of Descartes and Locke began 
to be felt; and that the Port Royal "Art of 
Thinking," of which an admirable translation, with 
Notes and an Appendix, by Mr. Baynes, has re- 
cently been published, is far the best of the trea- 
tises on the subject which were in use during the 
eighteenth century. Throughout the work, I have 
kept constantly in view the wants of learners, 
much of it having been first suggested while at- 
tempting to expound the science in my own class- 
room. My highest ambition will be satisfied if it 
should be found to be of use to other teachers. 

Cambbidge, March, 1864. 



CONTENTS. 



CHAPTEE I. 

Pagb 

Psychological Introduction ....•••! 

Intuitions distinguished from Concepts . . . • • 1 

The Nature of Thought 10 

Relations of Thought to Language ' 16 

Mental Characteristics of Brutes 18 

The Formation of Concepts 19 

Language aids Thought 21_ 

And is often substituted for it 24 



CHAPTER II. 

Definition of Logic 30 

The Form distinguished from the Matter of Thought . • 31 
Universal distinguished from Special Logic . . . .34 

Divisions of the Science ....... 36 

Utility of the Study of Logic .38 



CHAPTER III. 

The Primary Axioms of Pure Thought . . . . .47 

These Axioms reduced to one Principle .... 48 

This Principle explicated into three Axioms . . . .49 

Analytic distinguished from Synthetic Thought ... 52 

The Principle of Synthetic Thought explicated . • . .53 

Hamilton's Postulate of Logic 55 



xu 



CONTENTS. 



CHAPTER IV. 

The Doctrine of Concepts 69 

62 
66 
70 
, 72 
75 
77 
84 
86 
90 



The Elements of a Concept 

The twofold Quantity of Concepts . . 

First and Second Intentions . . . 

The Relation of the two Quantities to each other 

Infinitated Concepts ..... 

The Quality of Concepts .... 

The Standards of Nominal and Real Definition 

The Relations of Concepts .... 

The Laws of Homogeneity and Heterogeneity 

Definition and Division 93 



CHAPTER V. 



The Doctrine of Judgments .... 
The Nature of the Copula .... 
The Predicables and the Categories . 
The Quantity of Judgments, Aristotelic Doctrine 
The Quality of Judgments, " " 

Quantity as afiected by Quality, " " 

The Relation of Judgments .... 
Conditional Judgments .... 
The Hamiltonian Doctrine of Judgments 
Explication of Propositions Into Judgments . 



105 
109 
112 
120 
123 
125 
127 
128 
132 
141 



CHAPTER VI. 

The Doctrine of Immediate Inference 148 

JEquipoUence or Infinitation . . . . . . 152 

Conversion . . . . • . • • • .156 

Hamilton's Doctrine of Conversion 160 

Opposition and Integration . . . . . . .162 

Conspectus of Judgments and Immediate Inference, Aristotelic 

Doctrine 166 

Hamilton's Doctrine of Opposition and Integration . . 168 



CONTENTS. 



XIU 



CHAPTER VII. 

Thb Doctbinb of Mediate Inference : the Abistotelio Anai^- 

TSis OF Syllogisms 174 

175 
, 180 
187 
190 
194 
197 
202 
207 
212 
215 
219 
222 
226 



The Canon of Categorical Syllogisms . . 
This Canon explicated into Six Bales 
Dictum de omni et nuUo .... 
Figure and Mood ..... 
Redaction to the First Figure . . . 
The Mood of a Syllogism . . . 
The Technicalities of Redaction exemplified 
Conditional Syllogisms .... 
Disjunctive Syllogisms .... 
Dilemmas or Hypothetico-Disjunctives 
Defective and Complex Syllogisms . . 

Sorites 

Conspectus of the Aristotelic Doctrine of Syllogisms 



CHAPTER VIII. 

The Hauiltonian Docteinb of Syllogisms .... 228 

Analytic and Synthetic Order of Enouncement . . . 228 

Reasoning in the two Quantities 234 

The Doctrine of the Figures 239 

The Unfigured Syllogism ....... 244 

Hamilton's System of Notation or Symbolization . . . 246 

The Number of Moods increased by Quantifying the Predicate . 251 

The worse Relation of Subject and Predicate . . . 253 

Hamiltonian Table of Moods ....... 256 

Falsity of the Special Rules demonstrated .... 259 

Applicability of the diflFerent Figures to Deduction and Induction 261 

Conditional Syllogisms reduced to Immediate Inferences . . 264 

CHAPTER IX. 



Of Fallacies 267 

Fallacies in dictione improperly so called .... 269 
Division of Formal and Material Fallacies . . . .271 
Syllogisms of more than Three Terms ; Ambiguous Middle . 272 



XIV 



CONTENTS. 



Undistributed Middle ; Composite and Divisive sense 
Illicit Process of the Major and Minor Terms 
The Sophism of Eubulides, the Liar 
Sophisms respecting the Quality of the Reasoning 
Violation of the Canons of Hypothetical Eeasoning 
Material Fallacies ; petitio principii . , , 
Fallacy of the Impossibility of Motion . 
Ignoratio denchi ...,.,. 
Argumentum ad ignorantiam i . . . 
Non Causa pro Causa; post hoc, ergo propter hoc . 
Ignava Ratio . ... . , . , 
Achilles and the Tortoise ..... 



278 
281 
288 
290 
293 
294 
296 
298 
300 
306 
309 
312 



CHAPTER X. 



Applied Logic 

Science formed by Analysis and Synthesis . . . 
Classification in Science ....... 

The Relation of Cause and Effect .... 

Necessary Cognitions a priori ...... 

These Cognitions not mere Laws of Thought . . 
Elements of our Concepts of Individual Objects . . 
The preliminary Classifications of Science . . . 
Science advances through the improvement of Classifications 
Failure of the attempts made to classify the Sciences . 



314 
317 
322 
324 
328 
330 
334 
340 
343 
346 



CHAPTER XI. 

Demonsteative Reasoning and Dbductivb Evidence , . 351 

Demonstration applicable to mere Concepts, not to Real Things 352 

Why Mathematical reasoning is demonstrative . . . 353 

Mathematical evidence not a mere perception of identity . . 359 

Distinction between Pure and Applied Mathematics . . 361 

The Conclusion not deduced from the Major Premise . . 362 

The only New Truth is that enounced in the Subsumption . 364 

Particular facts not learned, but proved, by Reasoning , , 367 

Difierent classes of Major Premises ..... 371 

Technical terms used in the Construction of Science . . . 374 



^ 



CONTENTS. XV 

CHAPTER XII. 

Ikdttction akd Analogy 376 

Want of Universality in the Sumption fatal to strict Beasoning 376 

Induction and Analogy are means for discovering Truth . . 380 

Difference between them illustrated ..... 381 

Analogy is Aristotle's Seasoning from Example . . . 382 

Analogy leads only to Probable Conclusions . . . 383 

Induction presupposes the correctness of previous Classifications 385 

Uniformity of Nature the basis of Induction . . . 383 

This Maxim not an Ultimate Fact 389 

And not first obtained by Induction ..... 391 

But derived from the Principle of Causality .... 395 

What is Physical Necessity 400 

All Induction proceeds by simple enumeration .... 401 

A universal Logic of Induction cannot be established . . 403 

A General Fact, a Law of Nature, and a Cause distinguished . 405 

How a Law of Nature is discovered 409 

Physical Causes proved by the Laws of Nature subsumed under 

them 414 

Induction discovers, the Law of Causality proves . . . 416 



CHAPTER XIII. 

The Socbces of Evidencb and thb Causes of Ebbob . . 419 

Intuition the basis of all Certainty 419 

Intuition of external objects as external 421 

Memory as a Source of Evidence ..... 423 

The art of Writing an auxiliary to Memory .... 426 

The experience of others a necessary aid ... . 427 

Testimony distinguished from Authority ..... 428 

And Veracity from Competency 430 

Hume's Argument against Miracles examined .... 432 

The Criticism of Tradition and Ancient Writings . . 433 

The Theory of Probabilities 437 

Moral Causes of Error 445 

^ \ 



LOGIC. 

CHAPTER I. 

PSYCHOLOGICAL INTRODUCTION. 

Intuitions distinguished from Concepts. — Mental Characteristics of Brutes. 
— Relations of Thought to Language. 

THE beginning of all knowledge is in single acts of tlie 
Perceptive or Acqmsitive faculty, each of which re- 
lates immediately to an individual object or event. Such 
acts are called Intuitions or Presentations ; the former is the 
more generally received appellation. Each Intuition gives 
us a knowledge of its object so far only as this object is 
perceived now and here, and also as it is one, or undivided, 
though not necessarily indivisible. To recognize, or know 
over again, the object as similar to another tiling perceived 
on a former occasion or m a different place, or to analyze it 
into its parts or attributes, or to refer it to a class of tilings 
previously known, and thereby to give it a common name, 
requires the aid of a different alid higher power of the 
mind. In receiving Intuitions, the mind exerts no conscious 
activity whatever ; it is passively receptive of any impres- 
sions that may be made upon it, and does not in any way 
consciously react upon or modify those impressions. It is 
like a mirror reflecting the objects that are held up before 
it, perhaps giving distorted or unfaithful images of them 
on accomit of tlie imperfections of its own surface, but hav- 

1 A 



2 PSYCHOLOGICAL INTRODUCTION. 

ing no power to change or in any way affect them by its 
own will. 

The impression made upon my mind by the portrait of a 
friend which I am now looking at, as it hangs before me, or 
by the sounds to which I am listening as they are struck 
upon a violin ; the image now present to my memory of the 
relative whom I have recently lost ; the picture of a water- 
fall in a wood which my imagination at this instant forms ; 
the consciousness which I have of the present state of my 
own mind ; — all these are Intuitions, as each one of them 
relates to a single object, and each is immediate^ — that is, 
it does not come through the intervention of any other state 
of mmd. But what is denoted by the word man^ sounds or 
waterfall, is not an Intuition, for it does not refer to one ob- 
ject only, but to many. Man, for instance, includes under 
it John, Thomas, William, and many others ; and it does 
not convey a complete image of any one of these persons, 
but only a partial representation equally apphcable to any 
of them. John, when considered simply as man, is not 
regarded as he really is, that is, as possessing all his indi- 
vidual attributes and peculiarities, but only as having those 
attributes which he possesses in common with all other 
men ; he is not viewed immediately, but only through the 
medimu of what is called a Concept, or ^Thought of what 
is common to many. These words, therefore, man, sound, 
waterfall, and all other common names, do not denote In- 
tuitions, but Thoughts. 

The Perceptive or Acquisitive faculty, through which 
we receive Intuitions, as it is a merely passive power, or a 
capacity of being affected in a certain way, constitutes what 
may be called the receptivity of the mind. The Thinking 
or Elaborative faculty, — i. e. the Understanding, — as it 
has no Intuitions of its own, but voluntarily reacts upon 
and modifies those received fi'om the Perceptive facility, 
comparing them with each other, and thereby combining 



I 



INTUITIONS DISTINGUISHED FROM CONCEPTS. 3 

them into one Thought, or disjoining them as dissimilar or 
incompatible, belongs to the spontaneity, or self-activity, of 
the intellect. 

In the ordinary exercise of oiir faculties, Intuitions are 
so intemiingled with Thoughts, so quickly pass into them, 
and are so closely connected with them, that it is difficult 
to illusti'ate the distinction between the two by giving an 
example of an Intuition so isolated and peculiar that there 
will be no danger of confomiding it with any portion of a 
voluntary and more complex process of mind. But a good 
illustration may perhaps be foimd in the case, so frequently 
referred to, of a person bom entirely blind, and subsequent- 
ly enabled by a surgical operation, for the first time, to see. 
Suppose that the first visual sensation given to such a person 
were that of a flash of red light. This sensation, it is evi- 
dent, would be to him enthely peculiar or 8u% generis. He 
could not, at first, refer it to any class of things with which 
he was formerly acquainted ; he could not give it a name ; 
he could not analyze it into parts or attributes. He did 
not will to produce or to modify it ; it comes to him, so to 
speak, of its own accord. He could Tmoiv it, but not recog- 
nize it, as the presentation of an enthely new object, by 
which his mind was involuntarily affected in a new and sur- 
prising manner. Such, we may suppose, are the Intuitions 
of brutes ; and the faculty of Intuitions, as the Perceptive 
or Acquisitive faculty may be called, — a mere receptivity^ 
unmodified by any voluntary act of the patient, — is proba- 
bly the most prominent of the few mental powers which 
brutes possess in common with man. In respect only to 
Intuitions produced in him by external causes, man has no 
advantage over the lower animals. 

But although all our knowledo-e begins in Intuitions, it 
does not end vdth them. In man, the mere receptivity of 
mind is so soon modified by its spontaneity, — the mere In- 
tuition so quickly passes into voluntary or consciously active 



4 PSYCHOLOGICAL INTRODUCTION. 

Thought properly so called, — that we can hardly tell where 
the one ends and. the other begms. To recur to the case 
just mentioned ; the moment the person who has now first 
received his sight begins to consider or reflect upon the new 
presentation that has thus been made to him, he probably, 
in a certain sense, recognizes it as a new sensation^ — that is, 
he refers it to a class of feelings with which he was former- 
ly acquainted, as coming to him through the other senses, 
and which, as similar in some respects, though different in 
others, he has ranked together and called by one name, 
" sensations " or " feelino-s." Such recoo-nition is an act of 
Thought properly so called. It includes comparison of this 
Intuition with others, and a conscious discrimination of 
those respects in which it is similar to others from those in 
which it is unUke them. The Perceptive faculty gives us 
Intuitions of single objects, each of which is to us a distmct 
unit, having no connection or relation with anything else ; 
the Understanding, a higher faculty, gives us Thoughts, or 
enables us to analyze each thing into its parts or attributes, 
and thus to recognize its various points of resemblance and 
difference, and so to form classes of things. The former 
power furnishes the rude material — "the Matter," as it 
is technically called — of our knowledge ; the latter supplies 
" the Form," elaborating and disposing this rude material 
in a systematic way, or accorduig to regular laws, by tln^ow 
ing it into groups, so as to render it conceivable to Thought. 
Hence the Understanding has been called the unifying 
facidty, by which the many is reduced to unity. 

If we look out of a window for the first time upon a 
landscape that is entirely new to us, the momentary glance 
gives us only an Intuition of the scene, or a confused knowl- 
edge of it as one whole, without any distinction of parts, 
and without recognition of any of these parts as former 
objects of knowledge. This is because the Understanding 
requires time to do its work. But if we dwell long enough 



INTUITIONS DISTINGUISHED FROM CONCEPTS. 5 

upon the scene, first, we recognize (or know over again) 
one familiar set of objects, and call them trees ; then, other 
classes of objects previously kno^vn, and call them respec- 
tively buildings, rocks, hills, &c. Lastly, we consider the 
relations of these objects and classes of objects to each 
other and to similar objects fonuerly known, in respect to 
distance, magnitude, color, &c. , and are thus enabled to 
think the landscape as a whole. Tliis Thought contains a 
far more perfect knowledge than the Intuition, which was 
all that the senses gave us at the first momentary glance. 

Now, how much is implied in the successive recognition 
of the component parts of this knowledge as objects previ- 
ously known, and therefore appropriately designated by a 
famihar name ? Of course, as the landscape is supposed to 
be now seen for the first time, we do not recognize any in- 
dividual tree, building, or hill in it as precisely the same 
object that we have formerly seen. We mean only that 
we recognize it as similar to some fonner objects of knoAvl- 
edge ; that is, having seen many objects wliich agreed with 
each other as similar in many of their parts, — as possessmg 
trunks, branches, and leaves, — we have formed them into 
one class, and called them trees. The object in the new 
landscape is then recognized, not as famihar in itself, but as 
belonging to a familiar class of tilings ; we do not recognize 
it as an Intuition, but as a Concept, — not as this tree, but 
as a tree. Conception is that act of the Understanding or 
Thinking faculty whereby we unite similar objects into one 
class by overlookmg their points of difference and forming 
their common attributes into one Concept or Thought, the 
name of which thus becomes the common name of all the 
individuals included in the class. Here, again, the unify- 
ing office of the Understandhig appears ; the Concept re- 
duces the many to unity, — brings together many objects 
into one Thought or many attributes into one subject. 
Thus we are properly said to know many objects which we 



6 PSYCHOLOGICAL INTRODUCTION. 

have never seen ; for, through hearing or reading descrip- 
tions of them, we have formed a right Concept of what 
they are, and thus are enabled to recognize — i. e. know 
them over again — and call them by their appropriate name, 
when we do see them. But this evidently is only mediate 
knowledge, and is more or less imperfect and inadequate, 
depending on the scantiness or fulness of the Concept. 
As Mr. Mansel remarks, a Concept " is not the adequate 
and actual representative of any single object, but an inad- 
equate and potential representative of many." And again, 
" it is not the sensible image of one object, but an intelligi- 
ble relation between many." 

Concepts can never come to us from without, for the ex- 
ternal world has no Concepts. It has not even Intuitions 
or Percepts, but only real objects, — that is, persons and 
things, and their marks or attributes. Every real object 
has an indefinite or comitless number of such attributes ; 
for, however long and careftJly we may observe it, we can 
never be sure that we have ascertained all its elements and 
quahties. Carry the chemical analysis of it one step further 
than before, or place it in new relations with other real ob- 
jects, and it will manifest new properties or activities, the 
existence of which was formerly unsuspected. Observation, 
which proceeds by a series of Intuitions, can make known 
to us an indefinite number of these attributes, but can never 
exhaust them. Hence the knowledge which we can ac- 
quire by Intuition, though constantly increasing in ftilness 
and complexity, can never become complete, and is always 
attended with some uncertainty; as any conclusions that 
we form respecting the object may be vitiated by the pres- 
ence of a quality or element of whose existence we were 
ignorant. Moreover, the limited compass and finite powers 
of the human mind cannot take in at once all even of those 
attributes whose presence is perfectly known. The image 
or representation of the object in our minds unmediately 



t 



INTUITIONS DISTINGUISHED FROM CONCEPTS. 7 

becomes confused, when we attempt to make it grasp too 
much, or to comprehend, in truth, more than a very few of 
the known attributes. Giving up the attempt at complete- 
ness, then, we form a Concept of tlie object embracing 
comparatively few of its ascertained qualities, but selecting 
those which are most distinctive and essential, in order 
thereby more readily to discriminate it from other objects 
of a different class. Such a Concept is certainly incomplete, 
but it is clear in proportion to the narrowness of its dimen- 
sions. We can more easily grasp it in thought, and con- 
template it at once in its entireness, because it has so little 
complexity. On the other hand, the lack of fuhiess is apt 
to render the boundaries of the Concept somewhat less dis- 
tinct. Consequently, any object, so far as it is knoAvn only 
mediately^ or through such a Concept, is known only in a 
few of its leading attributes ; and it may even be doubtful 
whether another object, which resembles it in these attri- 
butes, but departs very widely fi'om it in others, ought to be 
ranked in the same class with it, and called by the same 
name, or not. If my Concept of tree, for instance, is limit- 
ed to these few particulars, — a vegetable organism possess- 
ing a main trunk, branches, and leaves, — it will be doubtful 
whether many small plants ought to be called trees or shrubs. 
But if I attempt to enlarge the Concept by introducing 
more attributes, so as to distinguish tree fully from all other 
plants, the idea becomes cumbrous and confused ; we can- 
not so easily embrace it in a single act of thought. 

While the Percept or Intuition belongs only to the par- 
ticular attribute or object — this one color, house, tree, or 
stone — which has impressed it upon the mind, the Con- 
cept refers to all the things whose common or similar at- 
tributes or traits it conceives (con-capio^, or grasps together 
into one class and one act of mind. Thus, for example, 
the Concept red color includes all similar red colors of any 
object whatever ; the Concept tree refers to all trees, the 



8 PSYCHOLOGICAL INTRODUCTION. 

Concept house to all houses, &c. And naturally enough ; 
for though the red or the white of this object is not the 
identical red or white of that object, — is at least numeri- 
cally different from it, and separated from it by the acci- 
dents of place and time, the one being perceived here 
and the other there^ the one being seen now and the other 
formerly^ — yet as the two produce exactly the same im- 
pression upon the mind, or create the same sensation, they 
are regarded as \drtually the same color for all the purposes 
of thought. Thus, also, though any one tree differs fi-om 
every other tree in many other respects besides the acci- 
dents of place and time, yet it is common to all trees to 
have a root, a trunk, branches, and twigs. Now as the 
Concept tree, is discriminated from all other Concepts only 
by possessing these four Marks or attributes, it must neces- 
sarily apply to all trees, which are regarded as the same for 
all the purposes of thought. And so it is with all Concepts. 
Hence they are also called Universals, or Gf-eneral Ideas. 

As Esser remarks, "A Concept is the representation of 
an object through its distinctive Marks ; — that is, not 
through those Marks which disting-uish it from other objects 
in general, but from those which come the nearest to it. 
The distinctive Marks of an object are evidently those 
which make it to be this object, and not some other one ; 
i. e. they are its peculiar and essential Marks. The com- 
mon and unessential Marks, therefore, do not necessarily 
belong to the Concept; if they were added to it, they 
would not only overburden and comphcate the Concept, 
but would lessen its applicability to other objects of the 
same Idnd. Hence it is self-evident how the Concept is 
related to the sensible Intuition. Namely, the Concept is 
the Intuition stripped of its contingent or miessential (in- 
dividual) attributes or Marks ; and the Intuition is the 
Concept clothed with the contmgent or imessential (indi- 
vidual) Marks." 



INTUITIONS DISTINGUISHED FROM CONCEPTS. 9 

A Concept may be derived from on« object as well as 
from many similar ones ; that is, it may not represent an 
actual, but only a possible, class or plurality of things. 
This may be illustrated by the description which a zoolo- 
gist would give of a "newly discovered animal, that was too 
unlike those formerly known to be included m the same 
species with any of them. Many shght pecuharities of 
such an animal would be passed over altogether, as unes- 
sential either to the class to which it belonged, or to any 
other. And of the more important Marks, wliich might 
be presuned to be specific and not individual in character, 
those only would be selected for careftil description which 
would serve to distinguish the new object fi'om those which, 
through their similarity in other respects, might be pre- 
simied to belong to the nearest species, or those most akin 
to the strange specimen. The description thus formed, 
containmg possibly not more than two or three Marks, 
would be at once a brief and clear Concept actually drawn 
fi'om an mdividual, but potentially a])plicable to a whole 
class, should other specimens of it be subsequently discov- 
ered. In a similar manner, the mmd may think any in- 
dividual object under a Concept consisting of a few well- 
chosen Marks, instead of knowing it simply by an Intui- 
tion as a conftised aggregate of many parts and elements, 
as brutes would do. We perceive only single tilings, for 
such only are jjresented to us ; we think only actual or pos- 
sible classes of things, for Nature does not give us classes, 
though she frirnishes us the resemblances of things, through 
which we proceed to classify them. All classification is an 
act of the mind, and is more or less arbitrary, depending 
on our selection of the attributes or relations in reference 
to which we classify them. 

It is evident that Concepts must be much clearer repre- 
sentations of things than the confused aggregate of Percepts 
or Intuitions on wliich they are founded. With their light 
1 * 



10 PSYCHOLOGICAL INTRODUCTION. 

they irradiate and make clearly intelligible everything to 
which they are referred, or with which they come together 
into consciousness ; and thus to explicate and make clear 
through Concepts the perceived or represented objects is, 
says Dressier, what it is, in the strict logical acceptation of 
the word, to think. In this sense, therefore, to think is to 
make clear through Concepts something already otherwise 
represented or known to consciousness. 

Esser says, " To think is to designate an object through 
a Mark or attribute, or, what is the same thing, to deter- 
mine a subject through a predicate." According to Sir 
William Hamilton, " Thought is the comprehension of a 
tiling under a general notion (Concept) or attribute " ; 
and agam, "All thought is a comparison, a recognition of 
similarity or difference, a conjunction or disjunction ; — in 
other words, a synthesis or analysis of its objects. In Con- 
ception, that is, in the formation of Concepts (or general 
notions), it compares, disjoins, or conjoins attributes ; in an 
act of Judgment, it compares, disjoins, or conjoins Con- 
cepts ; in Reasoning, it compares, disjoins, or conjoins Judg- 
ments. In each step of this process, there is one essential 
element; to tliink, to compare, to conjoin, or disjoin, it is 
necessary to recognize one thing through or under another ; 
and therefore, in defining Thought proper, we may either 
define it as an act of comparison, or as a recognition of one 
notion as in or under another." According to other logi- 
cians. Thought is the reduction of complexity and plurality 
to unity, or the bringing together of what is confused, vaii- 
ous, and manifold or multitudinous in our Intuitions into 
the clear unity of consciousness. 

All these definitions evidently point to one thing, or in- 
dicate what is substantially the same process. Comparison 
is the means through which we unite what is similar, and 
separate what is unlike or opposed ; for only through com- 
parison do we recognize likeness or unlikeness, agreement 



INTUITIONS DISTINGUISHED FROM CONCEPTS. 11 

or opposition. Now we analyze, divide, and distinguish 
only in order subsequently to bring together and combine. 
We discriminate the various elements or attributes of ob- 
jects through comparison of them with each other, and then 
miite them with other objects and attributes according to 
their similarities as ascertained by a fresh act of comparison ; 
and this union of many things in one class, this reduction 
of a plurality of Intuitions under one Concept or general 
notion, is the means through which the infinite variety and 
multitude of natxu'al objects are reduced to the limited com- 
pass of the human understanding, and made intelhgible. 
A new individual object is to us an isolated and incompre- 
hensible thing, until we have recognized its similarity with 
something else, and thereby assigned it to a class, or com- 
prehended it under a Concept, and given it a common 
name. 

According to some etymologists, thinh comes from the 
same root as thick* and originally signified thickening^ or 
pressmg together of many into one ; and this exactly de- 
scribes the special function of the understanding. As we 
have already remarked, while a Percept or Intuition is a sin- 
gle representation, limited to this one thing wliich excited it 
or impressed it upon the mind, a Concept is a collective (gen- 
eral or universal) representation of a whole class of things. 
To make a formal definition, we may say that a Concept 
is a representation made up from several particular Percepts., 
through the union of their similar eleme7its. It is through 
Concepts that we think, — that is, clearly miderstand, com- 
prehend, or conceive something ; for these words mean pre- 
cisely the same thing, namely, to represent with clearer 
consciousness what was already represented in our minds. 

Besides the Percept and the Concept, the later German 
philosophers distinguish the so-called Idea, as the pattem- 

* The n in think is casual, and does not appear in the participle thought. 
So in German, dick, denken, qedacht. 



12 PSYCHOLOGICAL INTRODUCTION. 

representation, ideal Concept, or heau-ideal, by wliicli we 
understand such a representation as sui'passes or goes be- 
yond the perceived and the conformed to experience. The 
Idea is that whereby we thmk an object in its highest possi- 
ble perfection, and consequently unHke anything which we 
have actually witnessed. Hence it does not refer, like the 
Intuition, to a single thing, nor, like the Concept, to a 
whole class of things ; but it wholly surpasses in complete- 
ness or perfection the object to which it is referred. Such 
are the Ideas of the artist, moral and religious Ideas, &c. 

The Kantians use Representations to designate the genus 
which includes, as its several species, Percepts, Concepts, 
and Ideas. The aggregate of the Percepts which any one 
has had may be said to constitute liis experience. 

Intuitions afford the only sure means of first creating, 
and of subsequently rectifying and enlarging, our Concepts. 
Thus, I may have some scanty knowledge, obtained by 
reading*^ perhaps, of a species of plant or flower that I have 
never seen. The Concept thus formed may err both by 
excess and defect ; by excess, because it may include some 
parts or attributes which are not peculiar to this species, but 
are common to it with many others ; by defect, because it 
may not comprise enough of the attributes common to all 
the plants in this class, and pecuhar to them or not belong- 
ing to any other plants, to enable me to recognize and dis- 
tinguish an individual of this species when I see it. It is 
only intuitive laiowledge, or that gained by direct observa- 
tion, which can enable me to correct these errors. 

Intuitions, then, are the only test of the reality of Con- 
cepts ; for they alone can determine whether the Concepts 
properly correspond to the actual objects in nature which 
they are meant to describe. In this sense. Intuitions are 
not only the beginning, but the basis and the source, of all 
our knowledge. All Concepts, however, are not meant to 
represent actual objects ; they may be imaginary or fanci- 



INTUITIONS DISTINGUISHED FROM CONCEPTS. 13 

ful. I can conceive a centaur or a griffin, though no such 
animal ever Hved. Yet even in this case, though the Con- 
cept, as a whole, is unreal or imaginaiy, it must be made up 
only of real parts or attributes, — that is, of such as have 
been embraced in some preceding Intuition. I have never 
seen a centaur ; but I have seen the head of a man and the 
body of a horse, and I can unite, in Thought, these real parts 
into an unreal whole. So, again, I can think or conceive . 
any combination, however fantastic, of colors that I have 
previously seen ; but I cannot introduce into the painting, 
even in Thought, any color that I have never seen. A 
person born bhnd, and remaining so, cannot conceive any 
color whatever ; just as one who has never had the sense of 
hearing can form no Concept of sound. Intuitions, then, 
are the basis, not only of all Knowledge, but of all Thought. 

The perception which gives us a new Intuition may take 
place either through the external senses, or exclusively 
through that mtemal source of knowledge, sometimes called 
an internal sense, but more properly denominated Con- 
sciousness, by which we are made aware of the existence 
of our own sensations, thoughts, and feelings. 

Consciousness, indeed, is the universal witness which 
testifies to the reality, not only of sensation and feeling, but 
of the external perceptions which come to us through the 
outer senses. I see a bright red color, I hear a particular 
sound, only so far as I am conscious of that act of seeing 
or hearing ; if I were not conscious of it, it would be to me 
as if it were non-existent. For to Icnoiv, and to hnoio that 1 
know, are phrases that designate one indivisible act of mind ; 
and to know that I know is a phrase which means the same 
thing as to be conscious. Hence, though it is an act of sense 
whereby I perceive the red color or hear the sound, it is at 
the same time an act of consciousness ; as, otherwise, I should 
have no knowledge either of the act of perception, or of the 
outward [)henomenon to the existence of which it testifies. 



14 PSYCHOLOGICAL INTRODUCTION. 

I am conscious also of internal perceptions, of hunger, 
pain, fear, joy, etc. Still further, I am conscious of myself^ 
as the one bemg that perceives, fears, or rejoices. Every 
act of consciousness is twofold, testifying to the existence 
both of the subject^ — that is, of the being or person who is 
conscious, — and of the object, — that is, of the feeling, per- 
ception, or other phenomenon of which he is conscious. 
The very language which I am compelled to use in making 
known the fact to another person testifies to this duality of 
the act. Any phrase used for this purpose must contain at 
least two terms, one expressive of the subject, and the other 
of the object, of consciousness. Thus, in the proposition 
" I feel hunger," the pronoun " I " denotes the person who 
feels, and " hunger " the phenomenon which is felt. In 
some languages, the whole may be expressed in a single 
word, as in the Latin " esurio " ; but the expression here is 
elliptical, the " ego," or the subject of consciousness, being 
always understood. The two elements can only be known 
together, simultaneously, and in their relation to each other. 
One is not known through the other, or in consequence of 
the other, or after the other ; but they are known together, 
in one act of mind. I cannot be conscious of hunger with- 
out, at the same moment and in the same act, being con- 
scious of myself as feeling the hunger. 

All the phenomena, then, both of the external and inter- 
nal world, are presented to the mind each in its distinctive 
or peculiar Intuition. In other words, any Intuition differs 
from every other Intuition, at least in the relations of time 
and space. Thus, two successive Intuitions by the same 
person, of the same thing, are distinguishable at least in this 
respect, that the one preceded the other, or took place at an 
earlier time. In hke manner, — to borrow an example from 
Mr. Mansel, — "I see lying on the table before me a num- 
ber of shiUuigs of the same coinage. Examined severally, 
the image and superscription of each is undistinguishable 



INTUITIONS DISTINGUISHED FROM CONCEPTS. 



15 



from that of its fellow ; but in viewing them side by side, 
space is a necessary condition of my perception ; and the 
difference of locality is sufficient to make them distinct, 
though similar, individuals." As already remarked, each 
Intuition is of a distinct thing as perceived now and here^ — 
that is, in its own pecuhar relations both to time and space. 
On the other hand, a Concept is freed from these relations 
of space and time ; I can think what is denoted by the 
word tree, Avithout identifying it with this or that particular 
tree, standuig on a particular spot, and seen at a particular 
time. 

As already remarked, it is the capacity of Thought prop- 
erly so called which constitutes the immeasurable superi- 
ority of the human over the brute mind ; but it is also true, 
that the necessity of Thought arises from the immeasurable 
inferiority of man's intellect to that of his Creator. If the 
human mind were omniscient and of infinite compass, it 
would behold all things intuitively, and would not be con- 
ftised and overburdened by the multitude of these single 
cognitions. But it is far otherwise ; the mind is limited 
and imperfect, and can grasp at once but few objects, — 
according to the common opinion, only five or six. It can 
permanently retain in memory, so as to reproduce at wiU, it 
can accurately represent m imagination, only a few of its 
primary Intuitions. We must have recourse to the artifice 
of Thought ; we must discard all ui dividual attributes and 
peculiai'ities, in order, through meagre Concepts, to rise to a 
larger and clearer, though consciously imperfect, compre- 
hension of a multitude of things. As will be shown here- 
after, it is precisely the scantiness of the general notion in 
respect to its import, which renders it more comprehensive 
in respect to the number of things which it embraces ; in 
other words, if we would know more objects, we must 
know each of them less perfectly. Unable to master the 
vastness and complexity of Natm'e by taking in detail the 



16 PSYCHOLOGICAL INTRODUCTION. 

objects whicli she offers to us, each in its separate Intuition, 
we throw them, through discarding their differences, into 
groups and classes. The muid can then grasp at once six 
or seven of these groups, instead of being hmited, as before, 
to six or seven individuals. Then, by forming successively 
groups of gi'oups, or classes of a higher order of generaliza- 
tion, our mental horizon is enlarged till we can take in, or 
comprehend (con-prehend/i)^ all the objects that we have 
ever known. But this is like ascending a very high moun- 
tain, whence, though we obtain a broader view, the outlmes 
and colors of objects below are but faintly seen, and many 
are wholly lost in the distance. 

The nature of Language illustrates this process of the 
formation of Thought. In fact, taken in its strictest sense, 
Language is the expression of Thought only ; it has to do, 
not with Intuitions, but with Concepts. Intuitions, from 
their very nature, can be designated only by Proper 'Names ; 
and words properly so called are Common Names. Every 
word has a meaning, and is therefore susceptible of defi- 
nition, or at least of explanation. But a Proper Name, 
strictly speaking, has no meaning ; as Mr. J. S. Mill re- 
marks, it is a sign which denotes this one thing, but Avhich 
connotes nothing. Like a pomting of the ^,finger, it desig- 
nates the individual who is meant ; but it says nothing as 
to the nature or character of that individual. In so far, 
indeed, as usage has limited one class of names to males, 
and another to females, in so far the names connote sex ; 
and precisely to this extent they cease to be Proper, and 
become Common, Names. If, to a person who does not know 
James, I say, " James did this," the effect is precisely the 
same as if I had said, " A main or boy did it." If a word 
is to express an Intuition, it must be accompanied by other 
words, or at least be marked by emphasis or a significant 
gesture, so as to restrict its meanmg to a determinate single 
thmg ; and these hmiting words can be dispensed with only 



RELATIONS OF THOUGHT TO LANGUAGE. 17 

when the context, or the custom of speech, supphes the 
necessary hmftations. For example : " tliis house now be- 
Ibre us," " that house on the hill," " the house in Cam- 
bridge which I showed you yesterday," are phrases wherein 
the general meaning of the word liouse is narrowed down 
to this or that particular building, which may be known 
through an Intuition. In other cases, the context or em- 
phasis suffices to limit the signification of such phrases as 
" his house," " John's house," " the house," etc., to the one 
thing which was intended. 

Dr. Reid puzzles himself in attempting to explain how it 
comes to pass, that, whilst all the objects and events which 
we perceive are individual or singular, all the Avords in a 
language are general. But the reasons are obvious. First, 
we cannot have comitless words for the innumerable single 
objects which we perceive, as no memory could retain 
them : — think, for a moment, of the mja-iads of leaves, 
blades of grass, insects, and other classes of things, which 
we are constantly beholding. Secondly, these very in- 
stances show, that, at least as far as our perceptions are 
concerned, the similarity of objects is often as great as their 
diversity, and even greater. Thirdly, one main pui'pose of 
language being the communication of Thought to others, 
what we need to know or to communicate is not so often 
a particular fact respecting this single object, as it is a gen- 
eral truth respecting a whole class of objects ; we do not so 
often need to say. Avoid or seek this one thing, as. Avoid 
or seek all of which this is a specimen. We are more fre- 
quently concerned, in our mental operations^ with classes 
than with incUviduals, though the latter alone furnish em- 
ployment for our hands. Fourthly, many things are usually 
massed together even to our perception, as individual trees 
in a forest, and therefore can never be exhaustively desig- 
nated by one expression. By the law of 'parsimony, there- 
fore, language makes up its millions of names or designa- 

s 



18 PSYCHOLOGICAL INTRODUCTION. 

tions out of comparatively few words, just as its thousands 
of words are constructed out of some twenty or thirty ele- 
mentary sounds or letters. 

Language, then, deals only with groups or classes of 
things ; and the process of classification necessarily pre- 
cedes the formation of language. This theory explains at 
once the most striking deficiency of the lower animals, — 
their incapacity of using language. As they have only 
Intuitions, the only names which they can apply or under- 
stand are Proper Names, — the appellations of this or that 
particular thing. These they can luiderstand. A dog can 
easily he taught toxknow the name of his master, even 
when pronounced by another person. They can even be 
taught to know the names of particular places and build- 
ings, so that they can understand and obey, when they are 
told to go to the barn, the river, or the house* But it is 
always the particular barn, or other object, with which they 
have been taught to associate this sound or significant ges- 
ture as its Proper Name. Carry the animal to a distant 
place, near which may be a set of corresponding objects, 
and then tell him to go to the barn or the river, and he will 
not understand the order as applying to the new set of 
objects, but will set off immediately for the old building or 
place, with whose Proper Name alone he is familiar. As 
Kant remarks, a dog knows (kennt^ his master, but does 
not recognize him through his peculiar Marks or Attributes 
(erkennt^, and thereby properly discriminate him from 
other persons. 

These Intuitions, which are common to man and the 

* In Mr. liockhart's amusing account of Sir Walter Scott's first favorite 
dog, " Camp," he says : " As the servant was laying the cloth for dinner, 
he would address the dog lying on his mat by the fire, and say, ' Camp, my 
good fellow, the Sheriff^ 's coming home hy tlie ford [or by the hill\' and Ihe 
sick animal would immediately bestir himself to welcome his master, going 
out at the back door or the front door, according to the direction given, and ad- 
vancing as far as he was able." 



MENTAL CHARACTERISTICS OF BRUTES. 19 

brute, and which are mere impressions passively received 
by the mind, may be stored up in the memory, but out of 
consciousness, as finiits of experience ; they may be subse- 
quently recalled to consciousness, or reproduced^ either by 
casual association or voluntaiy reminiscence ; and, when so 
recalled, they may be re-presented, or pictured forth to the 
mind, by an act of that faculty which we usually call Im- 
agination. Brutes, as well as men, are capable of all these 
acts of Memory, Reproduction, and Imagination, when ex- 
ercised upon Intuitions alone; for they are all implied in 
dreammg, and a dog asleep upon a rag before the fire often 
shows, by his barking and gi'owling, that he has vivid 
dreams. Man can remember and reproduce Concepts or 
Thoughts, as well as Intuitions. Imagination, whether in 
man or the brute, is concerned only with Intuitions, as it 
pictures forth nothing but definite images of this or that 
particular object or event. Thoughts properly so called 
are conceived or understood, but cannot be imagined* 

Agreeably to what has been said, the mental process of 
forming Concepts may be reduced to three steps, viz. : — 

1. Comparison, whereby, among many attributes or ob- 
jects, we determine wliich are similar and wliich are differ- 
ent or unlike. 

2. Combination or Reduction to Unity, whereby, for in- 
stance, this, that, and the other color are recognized and 
identified as what is usually called " one and the same " 
shade or hue of red ; or several quadrapeds are recognized 
as all belonging to one class called horse. 

3. Abstraction,^ whereby we separate and throw aside 

* If this simple distinction had been made, the old dispute between the 
Nominalists and the Realists could never have arisen. The former clearly 
perceived that Concepts could not be imagined; the Realists knew very well 
that, in thinking, our thoughts were concerned with something more than 
mere words. Both were right. 

f This word, according to its etymology {abs-traho, to draw ofF from), is 



20 PSYCHOLOGICAL INTRODUCTION. 

— i. e. put out of Thought — the dissimilar or incongru- 
ous attributes which, if retained, would prevent the other 
elements from flowing together into unity. • 

Each of these steps evidently involves an act of Judg- 
ment^ — that is, of that function of the Understanding or 
Thinking Faculty whereby we affirm or deny one Intuition 
or Concept of another. Hence, we may either consider 
Judgments as the elements of Concepts, or Concepts as 
the elements of Judgments. Logicians generally have 
treated of the functions of Conception or Simple Appre- 
hension first, and those of Judgment afterwards ; and, as 
this arrangement is in some respects more convenient, I 
shall follow their example, though strict method would per- 
haps require this order to be reversed. 

All men are capable of comparison, and of discerning 
those similarities on wliich the formation of Concepts de- 
pends. But it does not so readily appear how many differ- 
ent persons are naturally led to form the same Concepts, 
according as circumstances render them famihar with simi- 
lar classes of things. This is well explained by Dressier. 
Before the elements which are common to the constituent 
Intuitions can be really united into Concepts, they must be 
excited in consciousness simultaneously, or in immediate 
succession ; if they arose only separately, and at intervals, 
like disjoined fragments, there would be no mutual attrac- 
tion to draw them together. But when thus brought be- 
fore the mind at the same time, the synthesis of their 
common elements into one Concept is a perfectly natural 
process, in which we need no guidance, " as they flow to- 
gether by a sort of spontaneous attraction for each other, 

properly applied to the dissimilar elements which are put aside or aban- 
doned, though, until recently, logicians used it to designate the process of 
retaining and combining the similar elements. Sir W. Hamilton would say 
that we prescind the similar wliich is retained, and abstract the different wliicb 
is tlirown off. 



RELATIONS OF THOUGHT TO LANGUAGE. 21 

each of them being the object of a livelier and clearer con- 
sciousness than any of the dissimilar elements. For exam- 
ple ; if I see at once, or in quick succession, six different 
trees, I perceive their similar properties — i. e. root, trunk, 
branches, etc. — six times over, being once for each tree, 
and thus have a livelier or stronger consciousness of them 
than I have of those wliich, as dissimilar or peculiar to one 
tree, I pei'ceive only once. Moreover, for the very reason 
that these common elements are similar — that is, as they 
have fewer points of divergence or contrast — they more 
easily coalesce and melt into one Concept." As Hamilton 
remarks, " the qualities which by comparison are judged 
similar are already, by this process, identified in conscious- 
ness ; for they are only judged similar inasmuch as they 
produce in us indiscernible effects. " 

But this is not all. " The Concept thus formed by an 
abstraction of the resembhna; fi'om the non-resemblincr 
qualities of objects would again fall back into the conci- 
sion and infinitude from which it has been called out, were 
it not rendered permanent for consciousness by being fixed 
and ratified in a verbal sign." Hence, Language is neces- 
sary, not only that we may communicate our Thoughts to 
others, but that we may permanently retain and readily 
use these Thoughts for our own purposes. Concepts are 
factitious units, and the particular attributes which consti- 
tute them are somewhat arbitrarily selected, being more or 
less niunerous, and having greater or less resemblance, 
according to circumstances. A Concept, as we have al- 
ready remarked, cannot be pictured in Imagination ; and 
the presence of one of the real objects included under it 
does not necessarily suggest the particular attributes out 
of which it was formed, to the exclusion of others perhaps 
equally prominent to the eye. Hence, a Name must be 
given to it, wliich will be, of course, a Common Name for 
all the individuals contained under it; or the factitious 



22 PSYCHOLOGICAL INTRODUCTION. 

aggregate will be dissolved and lost to memory almost as 
soon as formed. The name preserves the unity of the 
aggregate just as it was originally constituted, precisely as 
a cord holds a bundle of things together, and enables us to 
handle many objects as if they were but one. The Mem- 
ory is then burdened with the retention only of one word, 
which, when recalled, by the law of association will suggest 
its meaning, instead of being urged to remember a consid- 
erable number of attributes, which can neither be sep- 
arately or collectively pictured in the Imagination. An 
Intuition, on the other hand, needs not to be designated 
by a Name, as the presence of the object immediattdy ex- 
cites it anew in its original perfection, and Imagination can 
re-present it almost as adequately and vividly as the reality. 
But the Concept can neither be retained in mind, nor, so to 
speak, readily manipulated in Thought, without the aid of 
a verbal sign. 

This mutual dependence of Thought and Language, 
each bearing all the imperfections and perfections of the 
other, has been admirably illustrated by Hamilton. 

" Though, in general, we must hold that language, as 
the product and correlative of thought, must be viewed as 
posterior to the act of thinking itself, — on the other hand, 
it must be admitted, that we could never have risen above 
the very lowest degrees in the scale of thought without the 
aid of signs. A sign is necessary to give stability to our 
intellectual progress, — to estabhsh each step in our ad- 
vance as a new starting-point for our advance to another 
beyond. 

" A country may be overrun by an armed host, but it is 
only conquered by the establishment of fortresses. Words 
are the fortresses of thought. They enable us to realize 
our dominion over what we have already overrun in 
thought, — to make every intellectual conquest the basis 
of operations for others still beyond. Or another illustra- 



RELATIONS OF THOUGHT TO LANGUAGE. 23 

tion : You have all heard of the process of tunnelling, of 
tunnelling through a sand-bank. In this operation it is im- 
possible to succeed unless every foot — nay, almost every 
inch — in our progress be secured by an arch of masonry, 
before we attempt the excavation of another. Now, lan- 
guage is to the mind precisely what the arch is to the tun- 
nel. The power of thinking and the power of excavation 
are not dependent on the word in the one case, on the 
mason-work in the other ; but without these subsidiaries, 
neither process could be carried on beyond its rudimentary 
commencement. Though, therefore, we allow that every 
movement forward in language must be determined by an 
antecedent movement forward in thought, still, unless 
thought be accompanied at each point of its evolution by 
a corresponding evolution of language, its further develop- 
ment is arrested. Thus it is that the higher exertions of 
the higher faculty of Understanchng — the classification of 
the objects presented and re-presented by the subsidiary 
powers in the formation of a hierarchy of notions ; the con- 
nection of these notions into judgments ; the inference of 
one judgment fi'om another ; and, in general, all our con- 
sciousness of the relations of the imiversal to the particular, 
consequently all science strictly so denominated, and every 
inductive knowledge of the past and future from the laws 
of nature : not only these, but all ascent fi'om the sphere 
of sense to the sphere of moral and rehgious intelligence — 
are, as experience proves, if not altogether impossible with- 
out a language, at least possible to a very low degree. 

" Admitting even that the mind is capable of certain ele- 
mentary Concepts without the fixation and signature of 
language, still these are but sparks which would twinkle 
only to expire ; and it requires words to give them promi- 
nence, and, by enabling us to collect and elaborate them 
into new Concepts, to raise, out of what would otherwise 
be only scattered and transitory scintillations, a vivid and 
enduring light." 



24 PSYCHOLOGICAL INTRODUCTION. 

But Words are not only signs and preservatives, they 
are also substitutes, for Thoughts ; and this peculiarity of 
Language is an excellence or defect in it, according as it is 
or is not judiciously used. As Bishop Berkeley remarks, 
" It is not necessary, even in the strictest reasonings, that 
significant names which stand for ideas should, every time 
they are used, excite in the understanding the ideas they 
are made to stand for. In reading and discoursing, names 
are for the most part used as letters are in algebra, in 
which, though a particular quantity be marked by each let- 
ter, yet, to proceed right, it is not requisite that, in every 
step, each letter should suggest to your thoughts that par- 
ticular quantity it was appointed to stand for." Having 
once satisfied ourselves, by spreading out in thought all the 
attributes which are combined in any Concept, — or, to be 
still more careful, by having once called up in Imagination 
a picture of some one individual possessing all these attri- 
butes, and therefore contained in the class, — that the 
meaning of the word, which is the Sign of that Concept 
and the Common Name of that class, is within our power, 
we proceed to use that word symbolically^ — that is, as a 
mere sign, and therefore with much more ease and rapidity 
than if it were necessary to stop, each time it recurs, and 
repeat the process of verifymg its meaning. Hence it may 
be said that the use of language gives us the power of 
thinldng in short-hand ; words are stenographic thoughts. 
Moreover, this abbreviated expression of thought is a great 
help to the memory. Having once ascertained by reflec- 
tion the relation of various Concepts to each other, — that 
is, having formed judgments and reasonings, and expressed 
them in propositions, — it is a far easier and shorter method 
to remember the few words which constitute such a propo- 
sition, than to recall successively each of the mental pro- 
cesses which are now embodied in it, and through which it 
was first obtained. Language is the great repository of 



KELATIOXS OF THOUGHT TO LANGUAGE. iio 

tliouglit, not only in oooks, but in onr own minds. The 
algebraist easily recalls to mind a few brief formulas, which 
enable liim to perform almost mechanically long numerical 
computations, which the mere arithmetician must slowly 
and pamfully tliink out step by step. Even when the 
meaning of the words is not sufficiently familiar to enable 
us to perform the whole process symbolically, or by the use 
of words alone, we can often do so in part ; — that is, we 
need only to explicate, or spread out in our minds, that 
particular portion of their meaning which happens to be all 
that is necessary for the special purpose which we now have 
in view. Thus I may not know the full meaning of a tech- 
nical term in some science, or of a certain verb in the Greek 
language, and still be enabled to use it without error in that 
one of its numerous applications with which use may have 
made me familiar. This STjmholic knowledge, as it was 
termed by Leibnitz, bears about the same relation to the 
full thought, of which it is the abbreviated expression, that 
our ordinary cursive handwriting does to an ideographic 
system, or to the picture-Avriting of the Mexicans. 

On the other hand, it should be remembered that there 
is peculiar danger in this use of words as a temporary sub- 
stitute for thought. Dr. Campbell mentions it as the rea- 
son why many persons, even among the judicious and the 
well-informed, ai'e sometimes led both to talk and write 
nonsense without knowing it. When the use of words is 
not checked by a frequent recurrence in thought to the 
precise limitations of their meaning, even the best of us 
are occasionally betrayed into applications of them which 
a moment's reflection would prove to be incongruous and 
absurd. The ordinary safeguard against such blunders is, 
that, having become familiar by use with certain words in 
tlieir ordinary relations and connections with other words, 
anything new or peculiar in the combinations in which they 
are sometimes found, or in which we may ourselves be 

2 



26 PSYCHOLOGICAL INTKODUCTION. 

tempted to place tliem, at once attracts our notice, and 
puts us upon the lookout to detect a possible absurdity. 
Take, for instance, the following stanza, which occurs in 
the " Song by a Person of Quality," written by Pope to 
ridicule this very class of blunders, as frequently committed 
by people of fashion in their attempts to strmg together in 
verse the mere commonplaces of poetical expression : — 

" Gloomy Pluto, king of terrors, 
Armed in adamantine chains, 
Lead me to the crystal mirrors 
Watering soft Elysian plains." 

As chains usually hind and mirrors reflect, not even the 
smoothness of the measure can here cause us to slide over 
the absurdity of supposing Pluto to be armed by the for- 
mer, or plains watered by the latter. 

To avoid such blunders, it is not enough to be able 
merely to explicate in thought the meaning of each word 
taken by itself, or separately, but the combination of words 
must express a possible union in thought of what is ex- 
pressed by them. Whether tliis can be done can be ascer- 
tained only through the process of what Mr. Mansel calls 
" individualizing our Concepts," — that is, of calling up in 
imagination a picture of some particular thing denoted by 
the words taken together, because possessing together all the 
attributes contained in such a union of Concepts. It is only 
by the failure of the attempt to form such a mental image, 
that we are led to perceive the absurdity of such expres- 
sions as a bilinear figure, an iron-gold mountain, or a water- 
ing mirror. Hence it appears, that what is perfectly intelli- 
gible in language, when the words are taken separately, 
may be absolutely inconceivable in thought. I know what 
each of the words bilinear figure means ; but such a figure 
is inconceivable, and therefore the union of the two words 
is absurd. 

It was remarked by Burke, in his Essay on the Sublime 



\'- 



RELATIONS OF THOUGHT TO LANGUAGE. 27 

and Beautiful, that words are not only used as substitutes 
for thoughts, but, through the laws of association, thev also 
serve to call up the same emotions wliich are naturally pro- 
duced by the presence or imagination of the real objects 
which they denote. Thus, there are many words which 
have feelings of awe, sorrow, or affright so firmly associ- 
ated with them, by long habit, that the mere utterance of 
them in a sermon is enough to solemnize the minds of the 
congregation, even before the hearers have time to tliink of 
what they mean. 

The doctrine of the Nominahsts, then, is true to this 
extent, — that very often, in the use of language, there is 
nothing before the minds either of the speakers or the 
hearers but mere words ; and yet these words are signifi- 
cantly and correctly used, and they answer their purpose 
of exciting emotion and imparting knowledge. But it is 
also often true, that, in the use of words, all the powers 
of the Understanding, or Thinking Faculty, are in active 
exercise ; — that we compare, combine, discriminate, judge, 
and discern new relations before unthought of, the subsidi- 
ary powers of the Memory and Imagination, all the while, 
furnishing their aid whenever needed ; and it is only by 
such concomitant activity of the Thinking power, that we 
can have fiill assurance that the words in question are cor- 
rectly used, and the boundaries of our knowledge are en- 
larged. Thus, in the thoughtful use of words, we are 
continually spreading out in our minds the attributes of 
which the Concepts are made up, individualizing them, 
comparing them with each other, discovering new relations 
between them, and carrying them up into higher orders of 
generalization, or extending them to more objects. 

A few remarks may be necessary in explanation of the 
nomenclature which has been here employed. The Eng- 
lish words tldnking^ thought, are commonly used, in a veiy 
vague and comprehensive sense, to denote any cognitive 



28 PSYCHOLOGICAL INTRODUCTION. 

act or object of the mind. But, as applied in Logic, they 
are strictly limited to one well-defined class of our cogni- 
tive functions. After the illustrations that have now been 
given, the peculiar characteristics of Thought properly so 
called are perhaps sufficiently understood. 

Hamilton justly observes, that most of the words which 
signify operations of the mind have a triple ambiguity, for 
they may denote either, 1. the faculty ; or, 2. the act ; or, 
3. the product of the act. To avoid this uncertainty, the 
Understanding is here used exclusively to denote the Fac- 
ulty of Thinking in the narrower sense, or what Hamilton 
calls the " Elaborative Faculty," because it elaborates, or 
works up into Thought, the raw material which is furnished 
to it by the Perceptive powers. Like any other faculty, 
the Understanding at any particular time may, or may not, 
be in exercise. Its function or peculiar office is to think ; 
hence, thinking denotes the act^ while Thought signifies the 
product^ of this faculty. As will be shown hereafter, 
Thought is the generic term, for there are three species 
of it; viz. Concepts, Judgments, and Reasonings or Infer- 
ences. The old logicians referred the origin of these tliree 
species of Thought to as many distinct faculties, which they 
denominated respectively Simple Apprehension, Judgment, 
and the Discursive Faculty. Of these, Simple Apprehen- 
sion corresponds very nearly to that sort of Thinldng which 
we now call Conception, its products being denominated 
Concepts. In like manner, the products of the Percep- 
tive or Acquisitive Faculty, hitherto called Intuitions, might 
more conveniently be termed Percepts, as we should then 
have an English verb, perceive, to express the act of that 
Faculty of Avhich these are products. If it were allowable 
to coin an English verb to express the act of intuition, an- 
swering to the German anscJiauen, analogy would direct us 
to say intuit. The Discursive Faculty (fi"om discurrere, to 
run to and fro) was so called because, in Reasoning or 



INTUITIONS DISTINGUISHED FROM CONCEPTS. 29 

drawinor Inferences, the mind runs over from one Judg- 
ment, as the Ground or Reason, to another, as the Conse- 
quence or Conchision, But the whole Understandhig is 
more properly called by this name ; for, in forming Con- 
cepts, the mind runs over the Percepts or Intuitions from 
which they are derived, in order to separate the similar 
elements from the unlike, and consciously to unite the for- 
mer into one product of Thought. 



DEFINITION OF LOGIC. 



CHAPTER II. 

DEFINITION OF LOGIC. 
Divisions of the Science. — Utility of the Study. 

LOGIC is the Science of tlie Necessary Laws of Pure 
Thought. 

The Greek word, \6yo^, from which Logic is derived, 
signifies both the inward thought, and the word or outward 
form in which this thought is expressed ; and thus includes 
both the ratio and the oratio of the Latins. This fact, and 
the ihtimate connection which, as we have already seen, 
exists between Thought and Language, has caused some 
writers, especially those who adopt the Nominalist theory 
to its fiill extent, to maintain that " Logic is entirely con- 
versant about Language." But it is not so ; for Logic is 
primarily and essentially conversant with Thought, and 
only secondarily and accidentally with Language ; that is, 
it treats of Language so far only as this is the vehicle 
of Thought. Just the reverse is true of the science of 
Grammar, which treats primarily of Language, and only 
secondarily of Thought. Logic might be called the 
Grammar of Thouo-ht. 

Others have held that " the process or operation of rea- 
soning is alone the appropriate province of Logic." But 
this is putting the part for the whole, and is as inadequate 
as it would be to restrict Geometry to the measurement of 
spherical bodies, to the exclusion of lines, angles, plane sur- 
faces, and rectilinear sohds. There are three classes of the 
products of Thought, namely, Concepts, Judgments, and 



DEFINITION OF LOGIC. 31 

Inferences or Reasonings, with each of which Logic is im- 
mediately concerned, as, indeed, no one of them can be 
adequately discussed without consideration of both the oth- 
ers. If, on the one hand, it can be said that conception 
and judgment are both subsidiary to the process of reason- 
ing, so, on the other, judgment is the primary and essential 
operation, of which conception and inference are only spe- 
cial forms or complex results. 

Pm'e, or, as it is sometimes termed, Foi'mal Thought, is 
the mere process of thinking^ irrespective of what we are 
thinking about. It has already been said that the Acquisi- 
tive or Perceptive Faculty furnishes " the Matter," while 
the Understanding supplies " the Form," of our knowledge. 
Tliis distinction between Matter and Form is one of con- 
siderable importance in the history of philosophy. The 
former is the crude material or the stuff of which anything 
consists, or out of which it is made ; while the latter is the 
peculiar shape or modification given to it by the artist, 
whereby it has become this particular thing which it is, and 
not something else which might have been fashioned out of 
the same substance. Thus, wood is the Matter of the desk 
on which I am writing, whilst the Form is that which enti- 
tles it to be called a desk, rather than a table or a chair. 
Vocal sound is the Matter of speech, and articulation is its 
Form. It is evident that these are two correlative notions, 
each of which implies the other : Matter cannot exist ex- 
cept under some Form, and there cannot be any Form 
except of some given Matter. But though the two cannot 
actually be separated, the mind can consider each separately 
through that process, called abstraction, whereby the atten- 
tion is wholly given to the one to the exclusion of the other. 
We may think separately of the attributes which are com- 
mon to a whole class of Forms, disregarding altogether, for 
the moment, the Matter of which each of them really con- 
sists. Borrowing algebraic symbols, the Matter in each 



32 DEFINITION OF LOGIC. 

case may be designated by a letter of the alphabet, the pe- 
culiar significance of which is, that it stands for any Matter 
whatever, and not for any one in particular. Thus, A is B, 
is the Form of an affirmative judgment, wherein A and B 
stand for any two Concepts whatever. Hence, whatever is 
true of the general formula, A is B, will be true also of 
any such particular instances, as Iron is malleable., Trees are 
plants^ &c., wherein the Form is associated with some par- 
ticular Matter. In saying, then, that Logic is concerned 
only with the Forms of Thought, or Pure Thought, or 
Thought in the abstract, — for all these expressions signify 
the same thing, — we mean only, that what is Material in 
Thought is extralogical, and, as logicians, we have nothing 
to do with it ; just as the geometer has nothing to do with 
the particular diagram on the paper before him, except so 
far as it is a symbol, or universal Form, of all possible fig- 
ures of the same general character. As Hamilton remarks : 
" The objects (the Matter) of thought are infinite ; no one 
science can embrace them all, and therefore to suppose 
Logic conversant about the Matter of thought in general, is 
to say that Logic is another name for the encyclopaedia — 
the omne scihile — of human knowledge. The absurdity of 
this supposition is apparent. But if it be impossible for 
Logic to treat of all the objects of thought, it cannot be 
supposed that it treats of ant/ ; for no reason can be given 
why it should limit its consideration to some, to the. exclu- 
sion of others. As Logic cannot, therefore, possibly include 
all objects, and as it cannot possibly be shown why it should 
include only some, it follows that it must exclude from its 
domain tlie consideration of the Matter of thought alto- 
gether; and as, apart from the Matter of thought, there 
only remains the Form, it follows that Logic, as a special 
science of thought, must be viewed as conversant exclu- 
sively about the Form of thovight." 

Again, the definition of Logic assumes that the process 



DIVISIONS CF THE SCIENCE. 33 

of Thinking, like every other operation in nature, does not 
take place at random, but according to certain fixed Laws 
or invariable modes of procedure. There could be no com- 
munication of Thought from one mind to another, if the 
process of Thinking in all minds were not subject to the 
same general rules. We follow these laws for the most 
part unconsciously, as a distinct recognition of them is not 
by any means necessary for correct thinking ; just so, many 
persons speak and write correctly without any knowledge 
of the grammarian's rules. But they can be discovered 
through analysis of their results, and the business of the 
logician is to search them out and arrange them in order, 
just as the grammarian's duty is to set forth those second- 
ary laws of Thought which control the formation and the 
use of Language. Logic, says Dr. Thomson, " like philoso- 
phy, of which it is a part, arises from a reflection of the 
mind upon its own processes ; a logician is not one who 
thinks, but one who can declare Jiow he thinks." 

But here a distinction is to be made, for Logic takes cog- 
nizance not of the contingent, but only of the necessary 
and universal, laws of Thought. Psychology, as the science 
of the mental phenomena in general, includes, of course, the 
procedures of Pure Thought ; but it includes them only in 
their contingent and phenomenal character, as actually 
existing now and then, but not as necessarily existing at all 
times. Logic does not consider the subsidiary processes, 
such as Perception, Memory, and Imagination, through 
which we collect the materials for thinking. The operations 
of the Thinking Faculty are also contingently modified by 
the coexistence of other powers and affections of the mind ; 
they are obstructed by indolence, and warped by prejudice 
and passion. Logic does not regard these accidental per- 
versions of the Understanding, but takes into view only 
those fundamental and absolute principles, to which all 
Thought is necessarily subject, and which shine by their 



34 DEFINITION OF LOGIC. 

own light, as tliey cannot be transgressed except by the 
idiot or the madman. A violation of one of these Laws is 
not so much an error in Thinking, as a negation of Thought. 
They are axiomatic in character; that is, they cannot be 
proved or deduced from higher principles, for such proof or 
deduction would be itself an act of Thought, and therefore 
would presuppose the validity of the very principles which it 
was intended to guarantee. These Laws cannot be proved, 
but they can be enunciated and explained ; when under- 
stood, their truth is self-evident, for they rest upon the 
immediate testimony of consciousness. As necessary and 
universally known, they are never consciously broken ; but 
we may be betrayed into an apparent transgression of one 
or more of them, through an incautious yoking together of 
certain words or formulas of expression, without sufficiently 
tliiyiking of what they denote. Some Hiberiiicisms, as they 
are termed, are of this character. The judge, who, when 
puzzled by the ingenuity of two lawyers who were plead- 
ing a cause before him, exclaimed in a pet, " I believe 
you are both right," really violated that universal Law of 
Pure Thought, called the Principle of Excluded Middle, 
which declares that, of two contradictory propositions, one 
must be true, and the other false. Logic, as it proceeds 
from axiomatic principles, and derives none of its materials 
from experience, but considers only those laws which under- 
lie all experience and first render it possible, is a purely de- 
monstrative science, like algebra or geometry. It treats of 
those arguments only which are certain and irrefutable ; or 
if it indirectly considers some of those forms which come 
short of perfect demonstration, such as Analogy, Imperfect 
Induction, and Example, it is only for the purpose of test- 
ing them by a refei-ence to the standard forms the validity 
of which they presuppose, and which they endeavor, as it 
were, to approximate. 

Universal Logic considers the Laws of Thought m their 



DIVISIONS OF THE SCIENCE. 35 

application, not to this or that special class of objects, but 
to all objects whatsoever. This is the Logica docens of the 
Schoolmen, and contains the abstract theory of the science 
in its widest sense, without any of the Hmitations that arise 
from any special pui'pose or study which the thinker may 
have in view. It corresponds to the science of Universal 
Grammar, which treats only of those principles which be- 
long to language as such, and therefore are exemplified in 
all languages, putting aside altogether the peculiarities of 
Hebrew, Greek, German, or any other particular tongue. 
On the other hand, /Special Logic, or the Logica utens of 
the Schools, is the Logic of Mathematics, or the Logic of 
History, or of any other particular science ; consequently, 
it involves a consideration of the Laws of Thought so far 
only as they are exemphfied or involved in the processes 
of this one science. Herein Logic becomes subsidiary to 
the objects of the special inquiry which it is intended to 
promote or regulate. It presupposes a knowledge of those 
objects, and it forms an introduction to that inquiry. 
Hence, it is no longer Logic considered for its own sake, 
but it is Geometry, Histoiy, or some other science, consid- 
ered in a logical point of view. The discussion of it is 
therefore relegated to treatises on that science of which it 
forms a part, and for which it is a special preparatory study. 
Legal Logic is a part of the science of Law. Mathemati- 
cal Logic is an introduction or an appendage to pure ]\Iath- 
ematics. But, in what now lies before us, it is evident that 
we have to do only with Universal Logic, which is one, 
while Special Logic is multiform ; which is independent, 
while that requires an acquaintance with other objects of 
study and other modes of investigation ; which is a part of 
the Philosophy of Mind, or of Philosophy itself in its wider 
sense, while that is a portion of a comparatively narrow 
science. 

There are certain other portions of what has usually 



36 DEFINITION OF LOGIC. 

been called Logic, wliicli, though they do not properly 
belong to the science itself, yet, as they are generally dis- 
cussed, often at great length, in most treatises upon it, may 
properly be defined and explained here, while a full consid- 
eration of them may be regarded as an appendix to the 
body of the work. Properly speaking. Pure Logic termi- 
nates with the consideration of the three classes of prod- 
ucts — namely. Concepts, Judgments, and Reasonings — 
which are the elements into which all Thought is resolved. 
But Thought itself is subsichary to the attainment of knowl- 
edge, — that is, to Science. The question remains, then, 
after we have folly treated of Concepts, Judgments, and 
Reasonings, taken separately or considered in themselves 
alone, what use is to be made of them, taken together, 
in the construction of Science. A full answer to this ques- 
tion, hs it would involve a study of the objects of Science, 
— that is, of the matter of the special sciences, — evidently 
falls outside of the province of Logic. But a partial answer 
to it, regarding Science in its relation, not to the objects 
known, but to the knowing mind, may be considered as a 
natural appendage to Logic, as it embraces the conditions 
not merely of possible, but of perfect. Thought. Such an 
answer is usually called the Doctrine of Method, or Logi- 
cal Methodology. Pure Logic considers only the Neces- 
sary Laws to which all Thought must conform ; the Doc- 
trine of Method regards those rules and principles to which 
all Thought ougJit to conform in order to obtain its end, 
which is the advancement of Science. Pure Logic treats 
merely of the elements of Thought, while Logical Meth- 
odology regards the proper arrangement of these elements 
into an harmonious whole. All Method is a well-defined 
progress towards some end ; and the end in this case is the 
attainment of truth. Practically speaking, the Doctrine 
of Method is a body of rules or precepts looking to the 
proper regulation of the Thinking Faculty in the pursuit 



DIVISIONS OF THE SCIENCE. 37 

of knowledge ; and, as such, it necessarily lacks the pre- 
cision and the demonstrative certainty which are character- 
istic of the principles of Pure Logic. The Laws of Pure 
Thouo-ht are absolute : the merits of Perfect Thought are 
various, and attainable in different degrees, according to 
circumstances. 

Another distinction has been taken, in this science, be- 
tween Pure and Applied Logic, or, as Sir William Hamil- 
ton prefers to call the latter. Modified Logic. The former, 
as we have seen, considers the Thinking Faculty alone, as 
if it constituted the whole of the human mind, and there- 
fore as if its Laws and Products were unaffected by any 
collateral and distiu'bing influences, but were manifested in 
precisely the same manner by different persons. It takes 
no account of the defects and hinderances which obstruct 
the normal action of the understanding. Modified Logic, 
on the other hand, considers Thought as it is, and not 
merely as it ought to be. It regards " the Causes of Error 
and the Impediments to Truth by which man is beset in 
the employment of his Faculties, and what are the means 
of their removal." And yet it is a universal science, — as 
much so as Pui'e Logic ; — for it does not consider the Mat- 
ter of Thought. The obstacles and imperfections which it 
points out are not those which arise from the objects of in- 
quiry, but fi'om the inquiring mind. They are subjective 
or psychological causes of error. Lord Bacon is probably 
the first philosopher who attempted a systematic enumera- 
tion of the causes of error. He made a quaint classification 
of them, under the significant name of Idols, into the four 
genera of Idols of the Tribe, or the necessary faults and 
imperfections of the human intellect itself; Idols of the 
Den, which arise fi'om the special constitution, education, 
and habits of each individual man ; Idols of the Forum, 
proceeding from the defects of the language which we are 
obliged to employ as an instrument of Thought and a means 



/- 



38 DEFINITION OF LOGIC. 

of communication ; and Idols of the Theatre, or the various 
dogmas of ill-founded systems of philosophy which have 
found their way into men's minds tlnough tradition, negh- 
gence, and credulity. 

But Modified Logic is not properly called Logic, as it is 
a hranch of Psychology, which treats of the phenomena of 
mind in general, and not merely of the normal action and 
necessary laws of one special faculty, the Understanding. 
As Modified Logic, however, is nearly allied in purpose 
with the Doctrine of Method, both looking to the same 
general end, — the attainment of truth through the proper 
regulation of the Thinking Faculty, — the two may well 
be considered together, under the general name of Applied 
Logic, as a kind of supplement to the science properly so 
called. Moreover, the connection between Thought and 
Language being so intimate, as we have seen, that neither 
can exist without the other, it would be an injurious, and, 
in fact, an impossible refinement, in a Treatise on Logic, to 
try to avoid frequent reference to those mistakes in thmking 
which proceed from an incautious use of words. 

The utility of the study of Logic — at least, of Formal 
Logic — has been, perhaps, more generally doubted or de- 
nied, during the last two or three centuries, than that of 
any other recognized science. In England especially, ever 
since Bacon's time, but more particularly since that of 
John Locke, the study has been as unreasonably decried as 
it was, during an earlier period, unduly exalted. The 
popular voice has been against it, and, till within the last 
thirty years, it steadily lost ground even in the Universities, 
where the popular voice is not often heard or respected. 
This unjust depreciation of the study was due in great part 
to the extravagant pretensions formerly put forward in its 
favor. An age which acknowledged Bacon and Descartes 
to be its intellectual leaders was likely to scrutinize with 
extreme jealousy the claims of a science long held forth by 



UTILITY OF THE STUDY. &9 

its votaries as the science or art " of the right use of rea- 
son," or "of forming instruments for the direction of- the 
mind" ; as " the liead and culminating point of philosophy," 
" the art of thinking," " the medicine of the mind," " the 
lighthouse of the intellect," " ars artium et sdentia scienti- 
ai'um, qua aperta, omnes alice aperiuntur, et qua clausa, 
omnes alice clauduntur" Especially was this the case, as a 
dark shade had already been cast upon this boastful study 
by the rapid decline and visibly approaching extinction of 
those systems of philosophy, theology, and physical science 
which acknowledged the same parentage, and had long 
been associated with it in asserted pre-eminence and ex- 
clusiveness. 

Logic fared not much better in the hands of those, its 
later disciples, who abated the extravagance of its preten- 
sions, indeed, and, by throAving aside many of its technicali- 
ties and nice distinctions, rendered its aspect less abstruse 
and forbidding. But, still adhering to the opinion that its 
main purpose was to furnish practical rules for the guid- 
ance of the understanding in the search after tnith, they 
destroyed its unity, broke down the boundaries which sepa- 
rate it from Psychology, Grammar, and Metaphysics, and 
encumbered it with a mass of disciphnary precepts which 
would be out of j^lace anywhere but in treatises on practi- 
cal education. The authors of the excellent "Art of Think- 
ing," which commonly passes under the name of the "Port- 
Royal Logic," deemed it necessary to apologize even for 
the hmited space which they had devoted to the special 
doctrmes of tliis science, on the ground that " custom has 
inti'oduced a sort of necessity of havmg at least a slight 
knowledge of Logic " ; and they remarked, that, as the 
heads of chapters sufficiently indicated the topics considered 
in them, those of exclusively logical import might be omit- 
ted in the perusal without serious injury to what remained. 
** When we thought any matter might be of service in 



40 DEFINITION OF LOGIC. 

forming the judgment," they added, "we never scrupled 
to insert it, to whatever science it might belong " ; and, 
accordingly, "in this Treatise, the reader will find many 
things relating to Physics and Ethics, [still more, they 
should have added, belonging to Grammar,] and almost as 
much Metaphysics as it is necessary to know." This is 
equivalent to denying that Logic has any claims to be con- 
sidered as a distinct science, or that a thorough and sys- 
tematic evolution of its principles would be of any practical 
benefit. 

The ground of these misapprehensions is entirely re- 
moved by the view which has here been given of the 
province and the purpose of Logic. Its boundaries are 
clearly defined, its pretensions are moderate, and it accom- 
plishes all that it is intended to perform. As a Formal 
Science, it takes no account of the Matter of Thought, 
which is all derived from processes of observation or intui- 
tion that lie beyond its province. It is not concerned with 
the something that is known, but only with the manner of 
knowing it. It is not an org anon of discovery, then, or a 
means to be used for the extension of any science. It ana- 
lyzes the Laws of Thought ; but, as these Laws are neces- 
sary and universal, — that is, as they exist in full force even 
in the humblest and least-instructed intellect, — it does not 
profess to teach anything absolutely new, but only to bring 
out into distinct consciousness and scientific arrangement 
what exists or takes place implicitly in every mind. These 
Laws of Thought exist there in a latent or involved form ; 
and we follow their guidance unconsciously, just as a person 
who has learned to speak and write only by moving in good 
society, and following the example of others, uses language 
in strict conformity with grammatical laws, though he is 
unacquainted with these laws even by name. The test of 
the validity of any doctrine in logical science is, that those 
to whom it is now for the first time communicated imme- 



UTILITY OF THE STUDY. 41 

diately recognize it as nothing new, except in the form of 
statement, but as a principle to which they have always 
conformed ever since they began to iliirik. The purpose 
of Logic, then, is only to teach us how we always liave 
thought, and not any new mode of thmking, or new pre- 
cautions, through which we may avoid the errors to which 
we were formerly liable, or by which we may discover 
truths that were formerly unattainable. It has no counsels 
to give, except to urge careful and uniform compliance Avith 
LaAvs which CA^ery one admits to be authoritative and uni- 
versal, and to which he has always intended to conform. 
As Mr. Mansel remarks, the science adAases only the better 
performance of existing obligations, and does not attempt 
the imposition of new ones. "A treatise on Logic is not 
designed primarily to give men facility in the practice of 
reasoning, any more than a treatise on Optics is intended 
to improve their sight; and it would be as correct for a 
writer on the mathematical principles of Optics to entitle 
his work ' Optics, or the Art of improving defective Vision,' 
as it is for a writer on the principles of Logic to adopt for 
his title, ' Logic, or the Art of Reasoning.' " * 

Indirectly, indeed, the science may be regarded as a 
medicine of the mind. As it brings out into clearer con- 
sciousness the laAvs to which all just thinking must conform, 
the indistmctness and confusion of thought to Avhich Ave are 
all liable are dissipated, and the errors which often folloAV 
the symbolic use of language, or the substitution of words 
for thought, are exposed and eliminated. In these respects, 
Ave think rightly as soon as Ave have learned to think clear- 
ly ; for the necessary forms of the understanding goA'ern 
Avithout dispute, Avhen their applicability to the case in hand 
has become manifest. " The progress of the sciences," 
says Hamilton, " consists, not merely in the accumulation 
of new matter, but likewise in the detection of the relations 
* Introductioa to Aldrich's Logic, third edition, p. hii 



42 DEFINITION OF LOGIC. 

subsisting among the materials accumulated ; and the re- 
flective abstraction by which this is effected must not only 
follow the laws of Logic, but is most powerfully cultivated 
by the habits of logical study." As we spread out Con- 
cepts into their constituent Intuitions, or individualize them 
in particular Imagmations, their true relations to each are 
intuitively perceived, and inconsequence or contradiction in 
uniting them becomes impossible. All this, however, is 
but the elimination of Formal error ; the Matter of thought 
comes from other sources ; and for the mistakes which arise 
from limited observation, or imperfect induction, Logic has 
no remedy to offer. It guarantees the correctness neither 
of the premises nor of the conclusion, but only the validity 
of the inference from the former to the latter. Hence, 
what is formally correct may be materially false ; I may 
reason rightly from wrong premises to a false conclusion. 
On the other hand, as an error in the Form necessarily 
vitiates the whole process of Thought, it may certainly be 
said that Logic furnishes us with a negative criterion be- 
tween truth and falsehood. The blunders which it exposes 
are vital, but they are not those which are most insidious, 
or even of the most frequent occurrence. 

Truth is the agreement of a cognition with the object 
which it is intended to represent. Now Logic, as it takes 
no cognizance of the object, which is the Matter of Thought, 
is evidentl}^ incompetent to determine whether such agree- 
ment exists or not. But there is a preliminary question to 
be settled before we come to a consideration of the object ; 
we inquire whether the cognition agrees with itself, — that 
is, whether it is Fonnally correct. And this question Logic 
is competent to determine with absolute certainty. The 
Formal coiTectness of a cognition does not by any means 
insure its Material truth ; but as Kant remarks, it is to be 
regarded as a conditio sine qua non of such tnith. 

The high place which Logic once held among the proper 



UTILITY OF THE STUDY. 43 

studies of a University, and which within a few years it has 

welhiigh reclaimed, is vindicated by the great value of the 
effort which is necessary to master it, considered simply as a 
vigorous exercise of the understanding. Indeed, its chief 
function is disciplinary, for the effort to acquire it may be 
said to equal or surpass in value the subsequent use to be 
made of the acquisition. It is not of so much importance 
to knoAv, as it is to have sti'engthened and developed all the 
faculties in learning to know. No other study taxes so 
severely the power of abstract thought, and hence no one 
furnishes better preparatoiy training for the pursuit of all 
the sciences which do not consist mainly in accumulating 
facts and registering the materials thus obtained. 

Little needs to be said of the intrinsic dignity of the sub- 
ject. " Admitting," says Heinrich Richter, as translated by 
Hamilton, " that this science teaches nothing new, that it 
neither extends the boundaries of knowledge, nor unfolds 
the mysteries which lie beyond the compass of our reflective 
intellect, and that it only investigates the immutable laws 
to which the mind in thinking is subjected, still, inasmuch 
as it develops the application of these laws, it bestows on 
us, to a certain extent, a dominion over our thoughts them- 
selves. And is it nothing to watch the secret workshop in 
which nature fabricates cognitions and thoughts, and to 
penetrate into the sanctuary of self-consciousness, to the end 
tliat, having learnt to know ourselves, we may be qualified 
rightly to understand all else ? Is it nothing to seize the 
helm of thought, and to be able to tui'n it at our will? For 
through a research into the laws of thinking, Logic gives 
us, in a certain sense, a possession of the thoughts them- 
selves. It is ti*ue, indeed, that the mind of man is, like the 
universe of matter, governed by eternal laws, and folloAvs, 
even without consciousness, the invariable canons of its na- 
ture. But to know and understand itself, and out of the 
boundless chaos of phenomena presented to the senses to 



44 DEFINITION OF LOGIC. 

form Concepts, through Concepts to reduce that chaos to 
harmony and arrangement, and thus to estabhsh the domin- 
ion of intelhgence over the universe of existence, — it is 
this alone which constitutes man's grand and distinctive 
pre-eminence." " Our whole dignity," says Pascal, " con- 
sists in thought." 

It is also argued by Sir William Hamilton, with great 
force, that " Logic is fiirther useful as affording a Nomen- 
clature of the laws by which legitimate thinking is governed, 
and of the violation of these laws, through which thought 
becomes vicious or null. 

" It is said, in Hudibras, — 

' That all a Rhetorician's rules, 
Serve only but to name his tools ' i 

and it may be safely confessed that this is one of the prin- 
cipal utilities of Rhetoric. A mere knowledge of the rules 
of Rhetoric can no more enable us to compose well, than a 
mere knowledge of the rules of Logic can enable us to 
think well. There is required from nature, in both, the 
faculty ; but this faculty must, in both departments, be cul- 
tivated by an assiduous and also a well-directed exercise ; 
that is, in the one, the powers of Comparison must be exer- 
cised according to the rules of a sound Rhetoric, in the 
other, according to the rules of a sound Logic. In so far, 
therefore, the utility of either science is something more 
than a mere naming of their tools. But the naming of 
their tools, though in itself of httle value, is valuable as the 
condition of an important function, which, without this, 
could not be performed. Words do not give thoughts ; but 
without words, thoughts could not be fixed, hmited, and 
expressed. They are, therefore, in general, the essential 
condition of all thinldng worthy of the name. Now, what 
is true of human thought in general, is time of Logic and 
Rhetoric in particular. The nomenclature in these sciences 



UTILITY OF THE STUDY. 45 

is the nomenclature of certain general analyses and distinc- 
tions, which express to the initiated, in a single word, what 
the uninitiated could (supposing — what is not probable — 
that he could perform the relative processes) neither under- 
stand nor express without a tedious and vague periphrasis ; 
while, in his hands, it would assume only the appearance 
of" a particular observation, instead of a particular instance 
of a general and acknowledged rule. To 'take a very sim- 
ple example : — there is in Logic a certain sophism, or act 
of illegal inference, by which two things are, perhaps in a 
very concealed and circuitous manner, made to prove each 
other. Now, the man unacquamted with Logic may per- 
haps detect and be convinced of the fallacy ; but how Avill 
he expose it ? He must enter upon a long statement and 
explanation, and, after much labor to himself and others, he 
probably does not make his objection clear and demonstra- 
tive after all. But between those acquainted with Logic, 
the whole matter would be settled in two words. It would 
be enough to say and show, that the inference in question 
involved a circulus in concludendo, and the refutation is at 
once understood and admitted. It is in like manner that 
one la^vyer will express to another the ratio decidendi of a 
case in a single technical expression ; while their clients will 
only perplex themselves and others in their attempts to set 
forth the merits of their cause. Now, if Logic did nothing 
more than establish a certain number of decided and deci- 
sive rules in reasoning, and afford us brief and precise 
expressions by which to bring particular cases under these 
general rules, it would confer on all who in any way employ 
their intellect — that is, on the cultivators of every human 
science — the most important obligation. For it is only in 
the possession of such established rules, and of such a tech- 
nical nomenclature, that we can accomplish, with facility, 
and to an adequate extent, a criticism oT any work of rea- 
soning. Logical language is thus, to the general reasoner, 



46 DEFINITION OF LOGIC. 

what the notation of Arithmetic, and still more of Algebra, 
is to the mathematician. Both enable us to comprehend 
and express, in a few significant symbols, what would other- 
wise overpower us by their complexity ; and thus it is, that 
nothing would contribute more to facilitate and extend the 
faculty of reasonmg, than a general acquaintance with the 
rules and language of Logic, — an advantage extending in- 
deed to every department of knowledge, but more especially 
of importance to those professions which are occupied in 
inference, and conversant with abstract matter, such as The- 
ology and Law." 



THE PRLMARY AXIOMS OF PURE THOUGHT. 47 



CHAPTER III. 

THE PRIMARY AXIOMS OF PURE THOUGHT. 

HAVING defined Logic to be the Science of the Neces- 
sary Laws of Pure Thought, our first object must be 
to ascertain what are the Fundamental and Universal Laws, 
here called Primary Axioms, to which all Thought, as such, 
is subject. In the separate consideration, which will come 
afterwards, of the three classes of Thoughts, — namely. 
Concepts, Judgments, and Reasonings, — we may expect 
to find Special Laws or Rules which are applicable only to 
one or two of these divisions. Such Special Rules may or 
may not be derivative in character ; — that is, they may 
be either immediate inferences from the Primary Axioms 
which govern all the products of the Thinking Faculty, or 
they may be independent, as resting upon their own evi- 
dence. Of this hereafter. But our first inquiry must be, 
whether there are any Axioms of universal applicabihty, 
which underlie and govern every act and product of the 
human Understanding ; and, if there are such, to deter- 
mine their character and significance. 

If there are such Axioms, they must be few, meagre in 
import, not susceptible of proof, and recognizable by all as 
fj-miliar truisms, which have always implicitly directed their 
thoughts, though perhaps, on account of their very obvi- 
ousness, they have never been explicitly stated or dra-vvn 
out into distinct consciousness. They must have these 
characteristics, because they concern only the Forms of 
Thought, or the manner of thinking irrespective of what 



48 THE PRIMARY AXIOMS OF PURE THOUGHT. 

we are thinking about ; and as tliese Forms themselves are 
necessarily limited in number and narrow in significance, 
the Axioms which underlie them aU, and constitute their 
common features, must be still fewer and poorer in import. 
They cannot admit of proof, as their truth is presupposed 
in every act of reasoning, and therefore no argument or 
proof is possible unless their veracity is taken for granted. 
They must be recognized by all as mere truisms, because 
they are thus self-evident, and because their truth has been 
acknowledged and acted upon in every Form of Thought 
which we have ever exf)erienced. The First Principles of 
all the sciences are avowedly thus few and meagre, as is 
seen to be the case with the introductory axioms of Geome- 
try and Physics. With still more reason do we expect the 
First Principles of all Thought to possess this character, as 
they stand in the same relation to the axioms of the special 
sciences, that these axioms do to the most advanced theo- 
rems which have been built upon them, or which have been 
constructed by taking them for granted. 

After this explanation, we need not be sui'prised to find 
that all the Primary Axioms of Pure Thought are perhaps 
reducible to this single principle : — AU Thought must be 
consistent ivith itself. If it be inconsistent, — if, directly or 
indirectly, it contradicts itseF, — it is self-destructive, and 
the Thought is null. Thus stated, the principle is coinci- 
dent with that which is usually called the Law of Contra- 
diction, though, as Hamilton remarks, it ought rather to be 
termed the Law of Non-Contradiction. Practically speak- 
ing, every Thought which must be rejected as formally 
invalid — that is, which is radically vicious in Fonn, what- 
ever be its Matter — offends against this principle. By 
logicians generally, however, this principle has been expli- 
cated into three general Axioms, called the Law of Identity, 
the Law of Contradiction, and the Law of Excluded Middle. 
The ground of this explication may be thus set forth. 



THE PRIMARY AXIOMS OF PURE THOUGHT. 49 

The primary element of all Thought is a Judgment, 
which arises from a Comparison. Hence, all Thought 
must proceed either by affirmation or denial, as these are 
the only two possible forms of Judgment. Having com- 
pared any two Concepts with each other, we either perceive 
their identity, similarity, congruence, or some other relation 
whereby we affirm their union in one act of Thought ; or 
we perceive the opposite relation between them, such as 
diffi3rence, unlikeness, or incompatibility, whereby we deny 
one of the other. As any Concept can be compared with 
any other, and as the Judgment which follows such com- 
parison must either affirm or deny one of the other, there 
being no third form of Judgment conceivable, we have the 
Axiom which is usually called the Law of Excluded Third 
or Excluded Middle, — Lex Exclusi Tertii aut 3Iedii. 
Either A is B, or A is not B : if we make any Judg- 
ment, — that is, if we think at all, — one of these two 
must be true-; for no third fomi is conceivable. It has 
been enounced in various forms : — Of two contradictory 
judgments, one must be true ; Every predicate may be 
affirmed or denied of every subject ; Every conceivable 
thing is either A or not-A. Of course, A and not-A^ taken 
together, include the universe, — the universe not only of 
all that is actual, but of all that is conceivable ; for as not-A 
excludes A only and nothmg else, it includes the universe 
exce])ting A only. 

Still further : — Not only are affirmation and negation the 
only conceivable forms of Jiidgment, but, as contradictory 
opposites, they are absolutely incompatible or mutually 
destructive. The admission of one is tantamount to a 
rejection of the other. If taken together, they destroy 
each other, and the Thouglit is rendered null. We can- 
not affirm both A and not-A of the same thing. Here we 
have the well-known Law of Contradiction, more properly of 
Non-Contradiction, of which the formula is, A is not not-A. 

3 D 



50 THE PRIMARY AXIOMS a? PURE THOUGHT. 

Evidently tliis Law is the principle of all logical negation 
and discrimination. It has been variously expressed: — 
Contradictory attributes cannot be affirmed of the same 
subject ; What is contradictory is inconceivable. It is less 
correctly expressed in the adage, " It is impossible for the 
same thing to be and not to be." This is a maxim which 
concerns the Matter of Thought, and therefore we must 
add to it the material limitations, in the same place, at the 
same time, in the same respect, &c. It is a mistake, then, to 
maintain that the Axiom, " Contradictory attributes cannot 
be affirmed of the same subject," is not universally true, be- 
cause we can form such assertions as this : A man can he 
loth young and not-young, though not at the same time. In 
Logic, where we consider only the Form of the Thought, 
a Judgment must be expressed by the present tense of the 
verb to he; for what we affirm is not the past or future 
union of two real phenomena, but the present coexistence 
and agreement of two Concepts in the mind. Hence, the 
logical Judgment, this man is not young, is absolutely 
incompatible with the assertion, this man is young, though 
it is compatible with the very different assertion, this man 
HAS BEEN young. 

Once more : The formula, A is not not-A, proves, on 
reduction, to be the exact equivalent or consequence of 
this, A is A. Here we have the principle of affirmation 
and agreement, as the former was that of negation and dif- 
ference. If an object cannot be thought under contradic- 
tory attributes, it is because it has a definite character of 
its own, excluding one of the contradictories through in- 
cluding the other. " The universe of conceivable objects," 
to adopt Mr. Mansel's language, " embraces both A and 
nx)t-A ; it is only when definitely conceived as the one, that 
an object cannot be conceived as the other. Every object 
of thought, as such, is thus conceived by limitation and 
difl'erence ; as having definite characteristics by which it is 



THE PRIMARY AXIOMS OF PURE THOUGHT. 51 

marked off and distinguished fi'om all others ; as being, in 
short, itself, and nothing else." Here, then, we have a 
third Primary Axiom, expressed as the Law of Identity : 
Svery A is A ; Every object of thought is conceived as 
itself; Every thing is equal to itself or agrees with itself; 
Every whole is the sum of all its parts. 

Thus we have three Primary Axioms of Pure Thought, 
— the Law of Identity, the Law of Contradiction, and the 
Law of Excluded Middle, — all of which may be regarded as 
exphcations of the single rule, that all Thought must be con- 
sistent with itself, or as corollaries from this one principle, 
that Judgment, which is the basis of all Thought, proceeds 
only by affirmation and denial. The mutual dependence 
and correlation of these three Axioms may be flirther illus- 
trated thus. 

I can think any object only by placing it under a Con- 
cept, or Class-notion expressed by a General Term ; and I 
can do this only by recognizing that it possesses the attri- 
butes which belong to this Concept and are common to all 
the members of this Class (Law of Identity, affirmation of 
similarity or agreement) ; by discriminating it fi'om other 
objects which have different attributes (Law of Contradic- 
tion, negation of agreement) ; and both this affirmation and 
denial proceed by the Law of Excluded Middle, which de- 
clares, for each given attribute, that the one or the other is 
absolutely necessary. Either it does, or does not, belong to 
the object, and the object does or does not belong to the 
Class. In respect to the Laws of Identity and Contradic- 
tion, says Sir William Hamilton, " each infers the other, 
but only through the principle of Excluded Middle ; and 
the principle of Excluded Middle only exists through the 
supposition of the two others. Thus, the principles of 
Identity and Contradiction cannot move, — cannot be ap- 
plied, — except through supposing the principle of Excluded 
Middle ; and this last cannot be conceived existent except 



52 THE PRIMARY AXIOMS OF PURE THOUGHT. 

through the supposition of the two former. They are thus 
coordinate, but inseparable. Begin with any one, the other 
two follow as corollaries." 

Hence he symbolizes the three Axioms by a Triangle, 
thus : — 




C is either r or non-r. 



These three Axioms are sufficient for all purposes of ana- 
lytic Thought. There is, however, another large class of 
Judgments, which are dependent in part upon a fourth Ax- 
iom ; and, as a preliminary to the consideration of it, we 
must explain the difference between analytic and synthetic 
Thought. Kant was the first to bring this distinction into 
notice as one of great importance in philosophy. 

In an analytic Judgment, the Predicate affirms nothing 
which was not already, though implicitly, contained in the 
Concept which forms the Subject. We analyze a Concept 
into the Marks or attributes of which it consists, and then 
predicate of it one or more of these Marks. Of course, no 
other knowledge is requisite for forming such a Judgment 
than is already contained in the Subject itself, as the Predi- 
cate affirms nothing more than what is so contained. Thus, 
if I say. Body is extended, A circle is round, An equilateral 
triangle has three equal sides, I merely repeat, or state 
explicitly, Avhat is already implied in the very notion of a 
hody, a circle, and an equilateral triangle. But in the prop- 



THE PRIMARY AXIOMS OF PURE THOUGHT. 53 

ositions, Body is heavy, A circle is a particular section of a 
cone, A triangle is a figure the three angles of which are 
equal to two right angles, the Predicate adds something that 
was not previously knoAvn and included in the notion of the 
Subject. There must be some reason for such addition ; 
otherwise, all Thought which is not merely analytical in 
character would be arbitrary and inconsequent. Pure 
Thought, which deals only with the Form, and not with 
the Matter, of Thinking, does not ask what this reason is, 
and seeks not in any way to determine its character. It 
only demands that there should be some reason, — that the 
connections of Thought, or those reductions to unity in 
which all Thinking consists, should not be merely casual or 
capricious ; in which case, there would be no proper con- 
nection at all. 

Besides the first postulate of the Understanding, that all 
Thought should be consistent with itself, we have, then, this 
second demand, in reference at least to synthetic Judg- 
ments, that all Thought should be consequent ; that is, that 
it should never affirm or deny a union of two Concepts 
without any ground for such affirmation or denial. The 
sufficiency of this ground or reason is a material question, 
with which the logician, as such, has nothing to do. Leib- 
nitz was wrong, then, in denominating this principle that 
of " the Sufficient Reason." The limitation is superfluous, 
for the only reason required is one that will make the union 
of the predicate with the subject conceivable, — not an actual 
union of real things ; and the reason which is insufficient 
for this end is no reason at all. This axiom, which is prop- 
erly called that of Reason and Consequent, or the Condi- 
tion and the Conditioned, is expressed in the formula, affirm 
nothing without a ground or reason ; or, every affirmation 
must have a ground or reason why it is affirmed. 

As the former postulate was evolved into three Axioms, 
so this one may be explicated into two, such explication 



54 THE PRIMARY AXIOMS OF PURE THOUGHT. 

being, in fact, only a statement of the meaning of the words 
employed. The first of these derivative Axioms is, that to 
affirm the Reason or the Condition is also to affirm the Con- 
sequent or the Conditioned; for the Reason would not be 
the Reason unless the Consequent followed it. The second 
Axiom is, that to deny the Consequent is also to deny the 
Reason; for, again, if the Consequent does not follow, the 
Reason cannot exist, since the Reason means only that 
which necessitates the Consequent. The two Axioms are 
thus pithily stated by the old Logicians : Positd conditione 
ponitur eonditionatum, suhlato conditionato tollitur conditio ; 
or thus : A ratione ad rationatum^ a negatione rationati ad 
negationem rationis, valet consequentia. 

Observe, however, that the converse of these two Axi- 
oms does not hold good. To affirm the Consequent is not 
to affimi any given Reason, since the Consequent may have 
followed from some other Reason ; and the same considera- 
tion shows that it is not competent, from a denial of any 
given Reason, to infer a denial of the Consequent. The 
primary Axiom asserts only the necessity of some Reason 
or other, not of any one Reason. The explication may be 
thus summed up in a tabular form : — 

There must he a Ground or Reason for every affirmation. 

Affirming the Reason affirms also the Consequent. 
Denying the Reason, nothuig follows. 

Affirming the Consequent, nothing follows. 
Denying the Consequent denies also the Reason. 

Strictly speaking, this Axiom is applicable to all analytic, 
as well as to all synthetic Judgments, and therefore, like 
each of the other three Axioms, it is a Universal Law of 
Thought. But in the case of analytic Judgments this Ax- 
iom does not need to be separately considered or enounced, 
for the ground or reason to which it refers is contained in 



THE PRIMARY AXIOMS OF PURE THOUGHT. 55 

the Judgment itself ; we cannot tTiirik the latter without the 
former. Thus, we cannot think of body without extension ; 
and therefore, when we affu'm that hody is extended, the 
Judgment carries its own reason or justification along with 
it. But in synthetic Thought, as when we say that matter 
is compressible, we see no reason in the Thoiight itself why 
the attribute of compressibility should be affirmed of it, any 
more than ineompressibility. The Axiom of Excluded Mid- 
dle tells us that one or the other must be so prechcated, — 
that matter must be either compressible or incompressible. 
Another necessary Law of Thought — that of Reason and 
Consequent — forbids us to predicate either of these con- 
tradictories to the necessary exclusion of the other, without 
a ground for such preference ; and the reason in this case 
must be derived from some soui'ce exterior to the Judgment 
itself, as no analysis of the latter will afford any such reason. 
We may, indeed, predicate neither ; we may leave the 
Thought, so far as this pair of contradictories is concerned, 
wholly indeterminate. But if we affirm anything of it, be- 
yond what is already contained in it, there must be a reason, 
express or implied, for such affirmation. 

With obvious propriety, analytic Judgments are also 
called explicative, as they merely unfold, and thereby 
bring into clearer consciousness, what we already possess. 
By tliem our knowledge is cleared up and rendered ex- 
plicit, but is not at all enlarged. Synthetic Judgments, on 
the other hand, are properly called ampliative, as by them 
our sum of knowledge is increased. Each of these re- 
quires a reason, as otherwise its result would not be the 
enlargement of knowledge, but the caprice of ignorance. 

It is rightly observed by Krug, that the relation of Rea- 
son and Consequent is something diffi2rent from that of 
Cause and Effiict. It is true that Cause and Effi^ct, so far 
as they are conceived in thought, stand to each other as Rea- 
son and Consequent. But the converse is not true ; all Rea- 



56 THE PRIMARY AXIOJIS OF PURE THOUGHT. 

sons are not Causes, and all Consequents are not Effects. 
The two relations may be distinguished from each other as 
being respectively what the old logicians called the ratio 
cognoscendi and the ratio essendi. Thus, to take an exam- 
ple, the ground being wet is the Reason why I know that it 
lias rained ; this is the ratio cognoscendi^ and it is evidently 
a relation of one thought to another thought; though the 
wetness of the ground is certainly not the Cause of the 
rain, yet, because I know that the ground is wet, I am jus- 
tified in thinking that the rain has fallen. On the other 
hand, the falling of the rain is the Cause of the ground 
being wet ; this is the ratio essendi, and it is the relation 
of one real thing, or actual occurrence, to another ; and, as 
such, it is independent of any thought, as the one thing 
would still cause the other, though there were no mind to 
observe their connection. Hence, the relation of Reason 
and Consequent is a mere synthesis of thoughts ; the 
thought of wetness of the ground suggests, and, so to 
speak, justifies the thought of rain. But Cause and Effect 
expresses an actual union of physical events, the real exist- 
ence of the one compelling or necessitating the existence of 
tlie other. 

This seems the proper place to introduce what is called 
*' the postulate of Logic," — a precept which Logicians have 
always assumed, and acted upon in part, but which, before 
Sir William Hamilton's time, they never distinctly enounced, 
or carried out consistently in all its consequences. To adopt 
his language, — 

" The only postulate of Logic which requires an articu- 
late enouncement is the demand, that, before dealing with a 
judgment or reasoning expressed in language, the import of 
its terms should be fully understood ; in other words. Logic 
postulates to be allowed to state explicitly in language what 
is implicitly contained in the Thought." 

This assumption is grounded upon the two fundamental 



THE PRIMARY AXIOMS OF PURE THOUGHT. 57 

propositions already stated and explained, namely, that 
Logic deals only with the Form, and not with the Matter, 
of Thought ; and that it is concerned primarily with the 
Thought, and only secondarily with the accident of its ex- 
pression. The science claims, therefore, to fill up the gaps 
and elisions of ordinary discourse, wherein much is sacri- 
ficed to brevity of speech, and to pare down the complexity 
and redundance of rhetorical expression into logical sim- 
plicity and precision. For ordinaiy purposes, and for the 
Rhetorician's use, language is a vehicle for the rapid and 
effective commmiication both of Thought and feeling ; con- 
sequently, it deals much in hints and abbreviated forms of 
speech, taking for granted all that the reader's and hearer's 
mind will readily supply, and aiming only to bring his fac- 
ulties of reasoning, imagination, and emotion into play in 
the right direction. The Logician, on the other hand, 
seeks to express nothing but Thought ; and he aims to 
make language a perfect representative of the Thought in 
its simplicity and entireness. His proper function is to 
point out those minute but frequently recurrent elements 
of Thought, which, precisely because fi'equently recurrent, 
are elided or passed over in ordinary discourse. Of course, 
the expressions which he thus finds occasion to use will 
often appear awkward and redundant, tediously minute, 
and even tautological. But he is not responsible for their 
rhetorical demerits ; the only question for him is, whether 
they fully and correctly express all that is actually passing 
in Thought. Thus, the common form of argumentation is 
the Enthyraeme, which consists of but two propositions ; 
but its Logical form is the Syllogism, consisting of three. 
No one but a silly pedant ever speaks or writes Syllogisms, 
except in a treatise on Logic. But the only question is, 
whether everybody does not think Syllogisms whenever he 
speaks or writes Enthymemes. To take another instance, 
Hamilton's doctrine of the thoroughgoing quantification of 

3* 



68 THE PRIMARY AXIOMS OF PURE THOUGHT. 

the predicate has been objected to for this reason, among 
others, that the propositions which it vindicates are so awk- 
ward and unnatural, that they seem "got up for the purpose 
of seeing what one can doi" Perhaps so ; and yet the 
objection is an idle one. For if there are occasions when 
we must think affirmative Judgments with universal predi- 
cates, and negative Judgments with particular ones, the 
Logician's first duty is to express this fact, however awk- 
ward and even ludicrous such expression may seem. 



THE DOCTRINE OF CONCEPTS. 59 



CHAPTER IV. 



THE DOCTRINE OF CONCEPTS. 



1. Their Quantity ; 2. Their Quality ; 3. Their Relation; 4. Their Defi- 
nition and Division. 

A CONCEPT is a combination, or a reduction to unity 
in Thought, of those elements and quahties of the 
objects which we are tliinking of, whereby they are dis- 
tinguished from all other objects, and especially from those 
which, in other respects, are most similar to them.* These 
distinoTiishino; attributes, which are the elements of the 
Concept, are called its Marks ; for through them the ob- 
jects of Thought are determined, or known to be what 
they are, and discriminated from what they are not. The 
word, or General Term, which is the appellation of tlie 
Concept, is, consequently, the Common Name of all the 
objects that are included under it. It is a convenient use 
of language, (though the words are sometimes applied in 
a different manner,) to say that the word or Name connotes 

* The words Concept and Notion, often used as synonymes, are perhaps 
best distinguished etymologically ; — Concept {con-capere) as the grasping 
up together of a pluraHty of attributes into one Thought ; Notion (noscere 
notis, to know an object by its Marks), as the taking note of the several 
Marks or characteristics of an object. The meaning of Notion might, 
perhaps, be conveniently limited to the apprehension of any single Mark 
■ ^nota), while Concept signifies the comprehension of all the attributes which 
are characteristic of a certain class of things. Thus, I have a Notion of 
each of the Marks, cold-blooded, vertebrated, animal, breathing bi/ means of pills, 
and living in the water, taken singly ; and I have a Concept of them taken 
together, as the characteristic Marks of a Fish, or of the whole class of 
Fishes. As thus limited, N(5tions arc a subordinate class of Concepts. 



60 THE DOCTRINE OF CONCEPTS. 

the attributes or Marks which make up its signification,* 
and denotes the individual thino;s contained under it which 
possess those attributes. Thus, the name 3Ian connotes 
biped, two-handed, rational, animal, and denotes all indi- 
vidual men and classes of men. 

It has already been explained, that a Concept is not 
necessarily the Thought of an actual, but only of a pos- 
sible, class of objects ; that is, its name may actually 
denote only one thing, as, for example, the one animal, 
just discovered, of a species hitherto unknown. Hence, 
Esser was led to define a Concept as "the representation 
of an (one) object through its distinguishing Marks." But 
even in this case, the representation, in order to be a Con- 
cept, must be a partial representation ; that is, it must 
represent, not all the Marks, but only the distinguishing 
Marks. Thus it becomes the representative of a possi- 
ble class or plurality of things ; if other specimens sliould 
be subsequently discovered possessing these distinguishing 
Marks, the Concept would include them also. It is only 
when the object is immediately jorescn^ei^ before us either 
by the Senses or the Imagination, so that we have a 
Presentation or Intuition of it, as one whole, with all its 

* " As these qualities or modes are only identified with the thing by a 
mental attribution, they are called attributes; as it is only in and through 
them that we say or enounce aught of a thing, they are called predicates, 
predicables, and predicaments, or categories (these words being here used in 
their more extensive signification); as it is only in and through them that 
we recognize a thing for what it is, they are called notes, signs, marks, charac- 
ters ; finally, as it is only in and through them that we become aware that 
a thing is possessed of a peculiar and determinate existence, they are called 
properties, differences, determinations. As consequent on, or resulting from, 
the existence of a thing, they have likewise obtained the name of consequents. 
What in reality has no qualities has no existence in thought, — it is a 
logical nonentity ; hence e converso, tlie scholastic apliorism, non-entis mdla 
sunt predicata. What, again, has no qualities attributed to it, though at- 
tributable, is said to be indetermined ; it is only a possible object of thought." 
— Hamilton, Lectures on iMgic, Am. ed., p. 5.5; 



THEIR CONTENTS. 61 

attributes, that its Name is a Proper Name strictly so 
called ; for if it is present only in Thought, our repre- 
sentation of it is necessarily partial, as not including all its 
Marks, and its Name is then vu'tually Common, as the 
designation of a possible plurality of things. Thus, if I 
am contrasting in Thought two historical characters, as 
Cesar and Pompey, these two names to my conception 
become General Terms, as several individuals may each 
possess the few Marks which, for the purposes of this 
contrast, I attribute to those two old Romans. Gray's 
affecting lines may be attributed to any churchyard : — 

" Some mute inglorious Milton there may rest, 

Some Cromwell, guiltless of his country's blood." 

Still further ; not merely may a Concept actually denote 
only one thing, it may actually connote only one Mark. 
But here, as before, there is a possible plurality in actual 
unity. Thus, in the present state of my knowledge, my 
Notion or Concept of red color may be absolutely simple, — 
that is, it may have but this one Mark of redness. But 
additional acquaintance with the science of Optics would 
teach me that this red color is an element of white light, 
and that it has a certain degree of refrangihility, by virtue 
of which its position in the solar spectrum is at one end of 
the scale. Here are three additional Marks of red color. 
In like manner, every Concept, though actually simple, 
must be regarded as containing a possible plurality of 
Marks. I say, it must be so regarded ; for every Concept 
must denote some existing object, — existing, that is, either 
really or potentially ; and no such object can be conceived 
of except as possessing a possible plurality of Mai'ks. 
For every object can be conceived to be what it is, only 
by discriminating it from several things which it is not; 
and such discrimination is possible only through a plurality 
of attributes. 



62 THE DOCTRINE OF CONCEPTS. 

This will be more evident, if we consider for a moment 
the various kinds of Marks by which one Concept may 
be distinguished from another. The following enumeration 
of them, which might be much enlarged, is taken in great 
part from Esser. 

Marks are divided, — 1. Into affirmative and negative, ac- 
cording as we know through them either what the object 
is, or what it is not ; thus, rational is an Affirmative, im- 
perfect a Negative, Mark of Man. 2. Into internal and 
external, according as the Mark is attributed to the object 
either in and for itself, or on the ground of the relation 
in which it stands to some other object ; thus, biped is an 
Internal, Father or Son an External, Mark of Man. 3. 
Into permanent and transitory, according as they are al- 
ways, or only sometimes, found in the object ; thus, metallic 
is a Permanent, hot is a Transitory, Mark of Iron. 4. Into 
peculiar and common, according as they belong to these 
only, or also to other objects ; thus, right-angled is a Pe- 
culiar, plane-figure is a Common, Mark of a Square. 5. 
Into essential or necessary, and accidental or contingent^ 
according as they can, or cannot, be separated from the 
object; thus, rational is an Essential, learned an Acci- 
dental, Mark of Man. 6. Into original or immediate, and 
derivative or mediate, according as they are either Marks 
of the thing itself, or only Marks of other Marks of it ; 
thus, free-willed is an Original, able to compute hy numbers 
a Derivative, Mark of Man, the latter being only a con- 
sequent or Mark of rationality. 

We gain another view of the elements of a Concept 
by dividing them into, — 1. Kinds of Existence ; 2. QuaK- 
ties, or Modes of Existence ; and 3. Relations, or Forms 
of Intermediate Existence. 

First, in order to conceive, we must conceive some- 
thing, — i. e. some being or existence, — which, as an object 
of Thought, may be distinguished from other things, and 



THEIR CONTENTS. 63 

to which qualities can be attributed. If there is no such 
entity^ at the bottom of the Concept, to give it unity, the 
Thought is null; non-entis nulla sunt predieata. There 
are but two kinds of Being or Existence, one of which is 
thus necessarily presupposed in Thought ; namely. Real 
and Imaginary or Potential. One or the other must enter 
into every Concept, not as attributed to it, but as presup- 
posed in forming it. In other words, every Thought must 
be of some real or imaginary thing. 

Secondly, whatever exists must exist in some deter- 
minate mode ; that is to say, it must have one or more 
quahties. Being or existence, as defined above, includes 
all things, both real and possible ; hence, in order to think 
any particular thing, we must discriminate it from other 
things ; and we can do this only by attributing to it 
Qualities, or particular modes of existence. By presup- 
posing existence, then, we have a thing, or object of possi- 
ble Thought ; by giving to it qualities, we have a definite 
thing, or object of actual Thought. The thing exists in 
itself, per se ; the quality exists only in the thing, — that 
is, in something different from itself, per aliud, or, as the 
logicians say, per aecidens. 

Thirdly, a Relation exists neither in itself, per se, nor 
in the thing as different from itself, per aliud, but between 
the thing and some other thing with which it is compared. 
This intermediate state of existence is the only character- 
istic feature of Relations, whereby they are distinguished 
from other Quahties. The Relation does not merely result 
from a comparison and discrimination, for this is true of 
all Qualities ; but it only exists as between one thing and 
another, thereby necessitating a Thought of both. Thus, 
the Relation of Husband and Wife exists in neither of 
them, but between them, and can be apprehended only 
by thinking of the two together. 

" Every object," says Drobisch, " is thought as a deter- 



64 THE DOCTRINE OF CONCEPTS. 

minate object only through the Marks appertaining to it, 
by means of which it is comparable, in respect to its nature, 
with other things, and is distinguishable from them. AVith- 
out these Marks, it is only an indeterminate something, a 
thing or bemg without ftirther determination ; just as, on 
the other hand, these Marks have no independent being in 
and for themselves, but they can be separated only in 
Thought from the object in which they exist. In the 
Concept of the object, then, there is the Thought of 
an independent but indeterminate something, united with 
determinate, but (in themselves considered) dependent, 
Marks ; the Concept of the object is the union of the two. 
(Thus, my Concept of Man is a living, rational, organic 
SOMETHING, having a mortal hody and an immortal soul.^ 
The Marks are the manifold, the plurality, and the in- 
determinate something is that which gives unity to these 
Marks, in the Concept of an object. The Concept is com- 
plex, therefore, and admits of separation into its elements ; 
and this separation is called Analysis." 

It is obvious enough, that the distinction between Con- 
cept and Marks is not absolute, but relative ; they may 
be used interchangeably. Any Concept may become the 
Mark of some other Concept; and every Notion, which 
may appear in one Thought as a Mark, becomes in 
another an independent Concept. Thus, the Concept ani- 
mal is a Mark of man; and metal, which is a Mark of 
iron, is itself a Concept, including under it iron, tin^ 
lead, &c. The only distinction consists in the two dif- 
ferent uses which are made of them in Thought. If a 
Concept is used only as a means of determining some 
other Concept, and so without direct reference to the ob- 
jects or things which it denotes, it is a Mark ; but if used 
as a Class-notion of certain objects, and with only second- 
ary reference to the attributes or qualities involved in it, 
it is a Concept in the stricter sense. In other words, if 



THEIR CONTENTS. 65 

used connotatively, it is called a Mark ; if used denota- 
tively, it is called a Concept. 

The only law of pure Thought applicable to the forma- 
tion of Concepts is the Axiom of Non-contradiction. A 
Concept must not have contradictory Marks, as these de- 
stroy each other, and the Thought so far becomes void or 
null. Thus, looking only to the Form of Thought, to the 
Concept A may be attributed the Marks B, C, D, and so 
on without limitation ; but B and not-B cannot be so 
attributed. 

Looking to the Matter of the Thought, however, a 
further limitation arises. Considered in relation to each 
other, Marks are either Congi'uent or Repugnant; the 
former can, and the latter cannot, be attributed to the 
same Concept. Thus, sweet and red are Congruent, as the 
same apple may have both Marks ; but siveet and hitter 
are Repugnant, since they cannot be united in the same 
object. If the tyro should object, that one part of it may 
be sweet, and another part bitter, the answer is, that the 
two parts are two different objects. Marks are said to be 
Contradictory, when the one is a simple or direct negation 
of the other ; as sweet and not-sweet^ B and not-B. They 
are Repugnant or Contrary, when the negation is indirect, 
as when the one is denied, not directly, but by putting in 
its place, or in the same Concept, another Mark with Avhich 
it is incompatible. The mere Form of the Marks tells 
me whether they are Contradictory or not; but to know 
whether they are Congruent or Repugnant, I must know 
the Matter of the Thought, — that is, I must have re- 
course to experience. 

Again, if considered as mere Marks, or with reference 
to their connotation only, the attributes which are united 
in the same object are disparate Notions, for they are 
different without any similarity. This holds true of Con- 
gruent, as well as of Repugnant, Marks ; thus, sweet and 



66 THE DOCTRINE OF CONCEPTS. 

red are Disparate, for the quality of sweetness has no re- 
semblance whatever with that of redness. On the other 
hand, if considered as Concepts, or with reference to what 
they denote, they are properly called disjunct or discrete 
Notions, for they are only relatively different ; they have 
at least so much in common, that they can be co-ordinated 
under some higher Concept. Thus, sweet apples and red 
apples are so far similar, that they both belong under the 
Class-notion apples or fruits. It is only stating the same 
distinction in other words to say, that Disparate Notions 
are Congruent, for they can be united in the same Con- 
cept ; but they do not denote any objects. On the other 
hand, the Disjunct do denote Objects, but they are not 
Congruent, for they cannot be united m, but are only 
contained under, the same Concept. 

To apprehend still further the nature of Concepts, they 
must be viewed in three aspects. First, if considered in 
themselves alone, they have Quantity ; secondly, if con- 
sidered in reference to the mind or thinking subject in 
which they are conceived, they have Quality ; thirdly, if 
considered in reference to each other, they have Relation. 

1. The Quantity of Concepts. 

It follows from the definition which has been given, 
that a Concept is a magnitude or Quantity, and that this 
Quantity is twofold. First, it has a number of Marks, 
which are reduced to unity in Thought, because they are 
all conceived as inhering in one object or thing. This is 
its Quantity of Intension. Secondly, it denotes a number 
of objects, which are reduced to unity in Thought as one 
class or species, because each of them possesses all these 
Marks. This is its Quantity of Extension. Thus, the 
Intension of bird is a winged, feathered, vertehrated, biped, 
animal; in its Extension are contained all individual birds 



THEIR QUANTITY. 67 

and classes of birds, as eagles^ vultures, hawJcs, pigeons, &c. 
The plurality of objects which are denoted by the Con- 
cept are said to constitute a Logical whole, or the whole 
of Extension ; the plurality of Marks connoted by the 
Concept form a Metaphysical whole, or the whole of 
Intension. 

This distinction of Quantity has been expressed by Lo- 
gicians in various ways, which are here enumerated for 
convenience of reference, though the forms of expression 
already given will be adhered to in the present work. 

A Logical or Universal whole A Metaphysical or Formal whole * 

has Extension, has Intension, 
Breadth, Depth, 

Sphere ; Comprehension ; 

contains under it, contains in it, 

denotes, connotes, 
Objects, Marks, 

Things. Attributes. 

This twofold Quantity of Concepts enables us to under- 
stand the seemingly opposite assertions, that the Subject 
of a proposition is in the Predicate, and yet that the Predi- 
cate is in the Subject. With reference to the Quantity 

* Besides the Logical and the Metaphysical, three other sorts of wholes 
have been distinguished by Logicians. 

1. The Essential or Physical whole is that which consists of Matter and 
Form, or substance and accident, as its essential parts. The characteristic 
of this whole is, that, as its parts do not exist out of each other, they cannot 
be separated except in Thought. As Burgersdycli says, " the Form per- 
meates the Matter, and informs all its parts," so that Form and Matter are 
inseparable. 

2. The Mathematical or Integral whole, on the other hand, has parts 
which are external to each other, so that they can be divided asunder. 
Tliis is the case with geometrical figures, as the triangle, the parallelogram, 
and with the human body and the limbs. These have partes extra partes. 

3. A Collective whole, or whole of Aggregation, has its parts separate 
and accidentally thrown together ; as, an army, a heap of stones. 



68 THE DOCTRINE OF CONCEPTS. 

of Intension, the Predicate is in the Subject, inasmuch 
as it is but one of several Marks which make up our 
Notion of the Subject. Thus, man is animal; animal may 
be regarded as a part of man, because it is a part of the 
meaning of the word ; and, when taken in connection with 
the other parts, living, two-handed, rational, makes up the 
whole Intension of the Concept man. But in respect to 
the Quantity of Extension, man is contained under an- 
imal, — the Subject in the Predicate, — since he is but one 
out of many kinds, all denoted by this one General Term, 
or contained under this one Concept, animal. 

" We find two expressions in Aristotle, both of which 
are sometimes rendered by ' being in,"" — inesse. 1. vnapxeiv^ 
by which the Predicate is said to be in the Subject. Tlus 

is equivalent to Kanryope'iaOai. To A vndpxfi. navrl ra B == to 
A Karrj-yopflrai Kara nuvrbs rov B = ^ inest Omni B (j= A. is 

predicated of every B = All B is A^. 2. dvai kv, by which 
the Subject is said to be in the Predicate. A kanv iv SXa 
T6) B = Omne A est B (^All A is B^. This is exactly the 
reverse of Karriyopdrai.. The English language is defective 
in not having, like the Greek and Latin, a proper Copula 
to express the relation of Intension as well as that of Ex- 
tension. Thus the relation expressed by inrapxti and inest 
can only be strictly rendered into English by a circum- 
locution, ' A is a quality belonging to B.' With the ordi- 
nary Copula, both must be translated into the language of 
Extension." * 

Besides the Concepts which are formed fi-om individual 
things, by abstracting their diflPerences and uniting their 
common or similar elements, we can, by a perfectly similar 
process, form Concepts of Concepts ; and then, again re- 
peating this process, we obtain Concepts of these Concepts, 
and so on indefinitely. In this way, we have in each case 

* Mansel, Notes to Aldrich, p. 45. 



THEIR QUANTITY. 69 

a hierarcliy of Concepts, of which only the lowest in order 
directly denotes individuals, while all the others directly 
denote other Concepts or classes, and only mdirectly denote 
the individuals contained in those classes. Thus, spaniel, 
terrier^ Jiound, mastiff, &c. are Concepts of the first or 
lowest order, each of them directly denoting certain indi- 
vidual animals, whose common attributes have become, in 
Thought, the Marks of their class. Then, abstracting the 
differences of these classes, we have dog as a Concept of 
the second order, directly denotmg spaniel, terrier, &c., and 
indirectly denoting the same individuals as before. Having 
formed in a similar manner secondary Concepts of cat, wolf, 
fox, bear, &c., by comparing all of these with dog, abstracting 
the differences and combining the similarities, we obtain the 
tertiary Concept carnivora. Again, comparing carnivora 
with rodents, marsupials, ruminants, &c., we have a Con- 
cept of the next higher order, mammal, of which the Marks, 
forming the Intension, are vertebrate, viviparous, warm-blood- 
ed, animal, suckling its young. It is evident that we can 
go on in tliis manner, rising through Concepts successively 
broader and broader in generalization, till we reach the 
hmit of human Thought in the Concept thing, entity, or 
object of TJiought, which connotes nothing but existence 
(real or potential), and denotes everything. 

I have here mtentionally taken an illustration of the log- 
ical process of generahzation from Natural History, as the 
science in which classification is most extensive and precise, 
though with the disadvantage of introducing here a number 
of technical names peciiliar to that science, and with which, 
as belonging to the Matter of Thought, Logic has nothing 
to do. But every word in our language, or in any language, 
perfectly corresponds to one of these zoological technicah- 
ties, in that it occupies a definite place in some one of the 
countless hierarchies of Concepts which the human mind, 
for various purposes, has been led to form. The greater 



70 THE DOCTRINE OF CONCEPTS. 

part of our mental life is spent in generalizing by successive 
steps, — that is, in forming Concepts of Concepts ; — but 
always, except in the science of Logic, with special refer- 
ence to the particular things denoted by these Concepts. 
Logic, which deals only with the Form, and not the Matter, 
of Thought, needs a set of technicalities of its own, to de- 
scribe these steps of generalization, and all other processes 
of fure Thought, with reference, not to the things which 
they denote, but to each other and to the thinking mind. 
This is precisely the distinction, so famous in the Scholastic 
philosophy, between jirst and second intentions, — a distinc- 
tion which lias been ignorantly ridiculed by those who did 
not understand it, but which in itself is perfectly mtelligible, 
and is as necessary as other technical distinctions in science, 
all of which, before they can be understood, require a 
knowledge of the elements of the special science in which 
they are taken. The burlesque question, utrum chimcera 
bombinans in vacuo posset comedere secundas intentiones, is a 
good specimen of the fun which for a long time was heaped 
on the study of Scholastic Logic. 

A first intention or notion is a Concept, whether of a low 
or a high order, which denotes things. Thus, in the illus- 
tration just given, spaniel, dog, carnivor, mammal, — each 
and all denote certain animals ; they are First Litentions. 
On the other hand, a second intention or notion is a Concept 
which denotes ^rs!{ intentions — i. e. the former Concepts — 
in their relation, not to the things denoted, but to each other. 
Thus, if the three lower steps in every hierarchy of Con- 
cepts are denominated respectively. Variety, Species, Genus, 
then these three names, applicable not only to spaniel, dog, 
carnivor, but to every other corresponding set of three suc- 
cessive steps of generalization, express second intentions. 
" First Intentions," says Mr. Mansel, " as conceptions of 
things, are predicable of the individuals conceived under 
them. Thus we may say, ' Socrates is man, animal, &c.' 



THEIR QUANTITY. 71 

Second Intentions are not so predicable ; we cannot say, 
' Socrates is species, genus, &c.' So, when Genns is said to 
be predicable of Species, it is not meant that we can predi- 
cate the one Second Intention of the other, so as to say, 
' Species is Genus ' ; but that the First Intention animal 
is predicable of the First Intention man, the relation of the 
one to the other being expressed by the Second Intentions 
genus and species. For this reason. Logic was said to treat 
of second intentions applied to first.'''' * 

It is obvious that Second Intentions are the peculiar tech- 
nicalities of the abstract sciences of Logic and Grammar. 
In the physical sciences, we have to deal only with Con- 
cepts of things ; but Logic and Grammar need Concepts 
of our modes of thinking and speaking of things, so far as 
these modes are related to each other. Thus, we need the 
technical terms Genus and Species to express the relations 
in which the several Concepts, that form any one hierarchy 
or series, stand to each other. These relations are indicat- 
ed in the following table. 

* Notes to Aldrich, p. 20. 



72 



THE DOCTRINE OF CONCEPTS. 



Second Intentions, 
or Concepts of Con- 
cepts, as ttiought rel- 
atively to each other. 



Summum Genus. 

Species or subal- 
tern Genus. 



Species or subal- 
tern Genus. 



Species or subal- 
tern Genus. 



Speciea or subal- 
tern Genus. 



Infima Species. 



First Intentions, 

or Concepts of 

things. 



Thing or Entity. 
Animal. 



Mammal. 



Carnivor. 



Dog. 



Spaniel. 



Intension, 
or Marks connoted. 



Existing. 

Existing, organized, 
sentient. 



Existing, organized, 
sentient, suckling 
their young. 

Existing, organized, 
sentient, suckling 
their young, eat- 
ing flesh. 

Existing, organized, 
sentient, suckling 
their young, eat- 
ing flesh, digiti- 
grade quadruped, 
&c. 

Silky-haired, water- 
dog, having all the 
preceding Marks. 



Extension, 
or Objects denoted. 



Everything. 

Every Vertebrate, 
Mollusk, Artic- 
ulate, and Ra- 
diate. 

Every vertebrat- 
ed animal which 
suckles its young. 

Bears, wolves, 
foxes, lions, 
tigers, &c. 



Mastiffs, spaniels, 
hounds, terri- 
ers, &c. 



All individual 
spaniels. 



Put any other, an entirely different, series of First In- 
tentions in the place of those given in the table, ■ — take, 
for instance, the series Man., European, Frenchman., Paris- 
ian, — and it is evident that the relations of these Con- 
cepts also to each other will be correctly indicated by the 
same Second Intentions as before. Man is now the Sum- 
mum Genus, Parisian is the Infima Species, and the inter- 
mediate Concepts are the Subaltern Genera or Species. 

A mere inspection of the table also brings to light the 
one law of Thought which determines the Quantity of 
Concepts. It is, that Intension and Extension, the two 
Quantities of every Concept, are always in inverse ratio to 
each other. They must both be present ; there must be at 



*l 



THEIR QUANTITY. 73 

least a minimum of each ; for a Concept muse always con- 
note something and always denote something. But if we 
take a great number of objects, we can find but few attri- 
butes or Marks which are common to them all, while a few 
objects may have many common attributes. Looking at 
the table, we see that, in the Sumnium Genus, the Inten- 
sion is least : in the case there given, only one Mark — 
existing — is connoted; while the Extension is greatest, for 
the same Concept denotes everything. Descending from 
the Highest Genus, we see that the Intension steadily in- 
creases through the Subaltern Genera, while the Extension 
regularly diminishes. In the Lowest Species, the Intension 
is at its maximum, as Spaniel connotes all the Marks of the 
hio;her Genera and one or two additional Marks, and the 
Extension is at its minimvffli, as there are fewer Spaniels 
than Dogs^ still fewer than Carnivora, &c. It is only stat- 
ing the same law in other words to say, with reference to 
any one hierarchy or series of Concepts, that any increase 
of the Intension produces, ipso faeto^ a diminution of the 
Extension, and any diminution of the former an increase 
of the latter. Observe, however, that it is only the origi- 
nal and essential Marks of which we speak, when we say 
that the number of Marks is inversely proportional to the 
number of objects denoted. The Original Marks carry 
their Derivatives along with them by necessary implica- 
tion ; and therefore we do not really increase the Intension, 
but only render it more explicit, when we annex certam 
Derivative attributes which were not formerly expressed — 
perhaps not even thought — as belonging to it. Thus, the 
Intension of triangle^ as a plane figure having only three 
sides and three angles, is not at all enlarged by adding this 
Mark, the sum of these three angles being equal to two right 
angles, even though I now for the first time learn that this 
is their sum. Though I did not, therefore, previously thi^ik 
this Mark of the Concept, it did nevertheless belong to it 

4 



74 THE DOCTRINE OF CONCEPTS. , 

implicitly, or by necessary inference ; and hence its express 
recognition does not alter either Quantity. In like man- 
ner, it is only the Essential Marks which determine the 
boundaries of a Concept ; we do not enlarge the Intension 
of man as a rational animal^ by adding this Accidental 
Mark, sometimes learned. As for the Mark capable of 
learning^ that is a Derivative from rational. 

The metaphysical meaning of essence is, that internal 
constitution of a thing which makes it what it is, — which is 
not only the source of its attributes, but is necessary to its 
existence. In this sense, of course, no finite mind can 
attain to a knowledge of the Essence of any real thing 
whatever. Passing by the disputes on this head as be- 
yond our province, it is enough to say that Logic (which 
has nothing to do with "real things," as they belong to 
the Matter of Thought) considers the Essence of a Con- 
cept to be the aggregate of its Marks, or, in other words, 
the sum of the attributes which it connotes. Still further: — 
Formal Logic cannot inquire into the nature of these at- 
tributes, but designates them indifferently by letters of 
the alphabet, as being all of the same kind. It necessarily 
presupposes, as above stated, that only Original and Es- 
sential attributes are used as Marks of a Concept ; and 
hence it looks only to their number, and not to their 
quality. Therefore, the law is universal and absolute, — 
add or subtract a single Mark, and the Extension, or 
number of objects denoted, is thereby diminished or in- 
creased. Essential means inseparable or necessary ; take 
away an Essential attribute, and the Concept ceases to be 
what it was, and becomes another Concept with a wider 
Extension. Thus, from man as a rational animal, remove 
the Mark of rationality, which is Essential to him, and 
the remaining Concept is animal, which denotes all men 
and brutes also. 

Grcnerification, usually called Creneralization, is the pro- 



THEIR QUANTITY. 75 

cess of rising, through the successive abstraction of Marks, 
from lower to higher Concepts. It is so called because the 
lower Concept is relatively a Species, and the liigher one, 
to which we proceed, is relatively a Genus, having a wider 
Extension. Tlius, we proceed from the lower Concept 
Mammal^ which is in this relation a Species, to the higher 
Concept Animal^ which is in the same relation a Genus, 
by throwing out the Mark suckling their young. The 
name of this process, therefore, correctly indicates the act 
of becoming a Genus. 

The contrary process, of descending from higher to low- 
er Concepts through the successive assumption of Marks, 
is called Determination, — more properly /Specification, as 
it expresses the act of becoming a Species. It has been 
well said, that it is the process of " thinking out objects 
by thinking in attributes." Thus, we descend from the 
Genus 3IammaUa to the Species Carnivora, by throwing 
out all herbivorous animals, through bringing in the Mark, 
eating flesh. 

It has already been observed, in treating of the Axiom 
of Excluded Middle and its applications, that every pair 
of Contradictory attributes, A and 7iot-A, divide the uni- 
verse between them, as one or the other must belong to 
everything. Because a given attribute, A, can be affirmed 
only of a certain number of objects, it must be denied of 
all other objects ; and we may express such denial by 
saying, all these others are Not-A. Hence we have a 
pecidiar class of Concepts, called Negative or Privative, 
more properly Infinitated, of which the characteristic is, 
that they denote almost everything, and connote ' next to 
nothing,' — that is, nothing positive. Thus they afford a 
curious illustration of the law, that the two quantities of a 
Concept exist only in an inverse proportion to each other. 
Logically considered, the Extension of the Concept Not-A 
is infinite, embracing the universe of existence both real 



76 THE DOCTRINE OF CONCEPTS. 

and potential ; for the subtraction of a finite quantity, J., 
does not diminish infinity. Consequently, its Intension is 
zero ; for it does not connote any Mark, but only the 
absence of the Mark, A. 

Practically considered, however, or with reference to 
the Matter of the Thought, " the universe " in such cases 
is not thought absolutely, but relatively; it means only 
the totality of that class of objects which we are thinking 
of, and to which A belongs. Thus, the two Concepts 
Frenchman and not-Frenchman are not thought to include 
all things, (which, if taken strictly, they would do,) but 
only all men. In like manner, not-male, which, if rigidly 
construed, would denote every stock and stone, besides 
many animals, is actually thought merely as a synonyme 
for female, and so denotes only about one half of the ani- 
mal kingdom. Sometimes, the name is seemingly positive, 
but the Concept or thought is truly negative. Thus, 
parallels are lines that do not meet ; therefore, as two 
negatives destroy each other, not-parallel are lines that do 
meet, — a really positive Concept under a Privative or 
Infiuitated form. For this reason, some writers have ar- 
gued that infinite, i. e. not-finite, is not thought negatively, 
but positively ; for finite, meaning limited or bounded, is a 
restriction or negation of the magnitude which infinite/ 
asserts positively. On the other hand, it is maintained 
that the essence of Thought, as such, consists in limitation 
or resti'iction ; for we cannot think any object except by 
distinguishing it, through its peculiar Marks, fi'om other 
objects ; consequently, to deny this restriction or negation, 
is to deny that the object in question has any peculiar 
Marks, or that it is distinguished from other objects in any 
manner whatever, and thereby to reduce the Thought of 
it to zero. 



their quality. 77 

2. The Quality of Concepts. 

When considered in relation to the mind or thinking 
subject in which they are conceived, Concepts may be 
said to have Quality, according as they more or less 
perfectly represent to this mind the objects which they 
denote, and the Marks or attributes by which those objects 
are distinguished. The three virtues of Clearness, Distinct- 
ness, and Adequacy constitute the perfection of Thought. 
The corresponding vices, of course, which render Thought 
imperfect, are Obscurity, Indistinctness, and Inadequacy. 
The Quality of a Concept depends on the degree in which 
it possesses each of these merits or faults. 

It is evident, from this account, that the Quality of 
Concepts, depending on the characteristics not merely of 
possible, but of perfect^ Thought, properly belongs either 
to the Doctrine of Method, or to what Hamilton calls 
Modified Logic, rather than to Pure Universal Logic. As 
the subsidiary processes of Definition and Division, however, 
by which the Qualities of Clearness, Distinctness, and Ad- 
equacy are obtained, are applicable to all Concepts, and, 
in a certain degree, regulate their formation and use in all 
minds, there is sufficient reason for considering the subject 
here, instead of regarding it as a mere appendage to the 
science, to be treated only at the close. It is sometimes 
convenient to depart a little from a rigorously systematic 
arrangement, more being gained than lost by the sacrifice. 
For this reason, and even as a matter of necessity, several 
matters properly appertaining to the Relation of Concepts 
have been partially considered in the preceding section, 
under the head of their Quantity. The filiation and inter- 
dependence of the parts of a science are often such, that 
it is impossible to give a proper explanation of any one 
of them without presupposing some knowledge of the 
others. 



78 THE DOCTRINE OF CONCEPTS. 

A Concept, being the reduction of a plurality botii of 
Marks and Objects to unity, supposes the power of thinking 
one and many both separately, and in their relation to each 
other, or together. We think the Concept clearly as a 
unity, when we can clearly distinguish it as one M^liole 
from other unities, — that is, from other Concepts regarded 
as wholes. We think it distinctly as a plurality, when 
we can distinguish both the Marks and the Objects which 
constitute it from each other. The Clearness of my 
Concept of a given metal — iron, for instance — depends 
on the fulness and precision with which I distinguish it 
as one whole from other Concepts, especially of those 
substances which, like the other metals, tin, copper, plati- 
num, a's nearest or most similar, would be most likely to 
be confounded with it. The opposite of this merit is Ob- 
scurity. On the other hand, the Distinctness of a Concept 
depends on the fulness and precision whereby I apprehend 
it as a plurality, — that is, as connoting many attributes 
or Marks, which I clearly distinguish from each other, 
and as denoting many Objects, which also I can clearly 
distinguish from each other. The former, or the dis- 
tinct apprehension of the several Marks, is its Internal 
Distinctness ; the latter, the distinct apprehension of the 
several Objects contained under it, is its External Dis- 
tinctness. The opposite of this merit is Indistinctness. 

It is evident that these qualities of a perfect Concept 
may exist in an indefinite number of degrees ; and it is 
also evident, that a Concept may be quite Clear, whUe 
it is but very imperfectly Distinct. A young child may 
have a very Clear notion of a clock, as distinguished from 
the other objects in the room, and still have but a very 
Indistinct apprehension of its parts, properties, and uses, 
or of the various kinds of horological instruments all 
denoted by this name. On the other hand. Distinctness 
necessarily involves Clearness ; I cannot have a Distinct 



THEIR QUALITY. 79 

apprehension of all the Marks of a Concept, without being 
thereby enabled clearly to distinguish it as one Avhole from 
other Concepts. The fact, that we may be able veiy 
clearly to discriminate a whole fi'om other wholes, or a 
Concept fi'om other Concepts, though we can but indis- 
tinctly separate in thought the parts or the Marks which 
constitute that whole or that Concept, is thus illustrated 
by Hamilton, from the analogy of our Perceptive and 
Representative Faculties. 

" We are ah acquainted with many, say a thousand, indi- 
viduals ; that is, we recognize such and such a countenance 
as the countenance of John, and as not the countenance of 
James, Thomas, Richard, or any of the other 999. This 
we do with a clear and certain knowledge. But the coun- 
tenances wliicli we thus distinguish from each other are, 
each of them, a complement made up of a great number 
of separate traits or features ; and it might, at first view, 
be supposed that, as a whole is only the sum of its parts, 
a clear cognition of a whole countenance can only be re- 
alized through a distinct knowledge of each of its constitu- 
ent features. But the slightest consideration will prove 
that this is not the case. For how few of us are able to 
say of any, the most famihar face, what are the particular 
traits Avhich go to form the general result: and yet, on 
that account, we hesitate neither in regard to our own 
knowledge of an individual, nor in regard to the knowl- 
edge possessed by others. Suppose a witness be adduced 
in a court of justice to prove the identity or non-identity 
of a certain individual with the perpetrator of a certain 
crime, the commission of which he had chanced to see ; — 
would the counsel be allowed to invalidate the credibihty 
of the witness by, first of all, requiring him to specify the 
various elements of which the total likeness of the accused 
was compounded, and then by showing that, as the witness 
either could not specify the several traits, or specified 



80 THE DOCTRINE OF CONCEPTS. 

what did not agree with the features of the accused, he 
was therefore incompetent to prove the identity or non- 
identity required ? This would not be allowed. For the 
court would hold that a man might have a clear perception 
and a clear representation of a face and figure, of which, 
however, he had not separately considered, and could not 
separately image to himself, the constituent elements. 
Thus, even the judicial determination of life and death 
supposes, as real, the difference between a clear and a 
distinct knowledge : for a distinct knowledge lies in the 
knowledge of the constituent parts ; while a clear knowl- 
edge is only of the constituted whole. 

" Continuing our illustrations from the human counte- 
nance ; we all have a clear knowledge of any face which 
we have seen, but few of us have distinct knowledge even 
of those with which we are familiar ; but the painter, who, 
having looked upon a countenance, can retire and repro- 
duce its likeness in detail, has necessarily both a clear and 
a distinct knowledge of it. Now, what is thus the case 
with perceptions and representations, is equally the case 
with notions. We may be able clearly to discriminate one 
concept from another, although the degree of consciousness 
does not enable us distinctly to discriminate the various 
component characters of either concept from each other." 

Clearness and Distinctness, with their opposites, were 
first regarded as qualities of vision merely, being applied 
only to objects as seen, their signification being afterwards 
extended by analogy to the other senses, and finally to 
Thought. The distinction between them, first fully pointed 
out by Leibnitz, was admirably illustrated by Krug, in a 
passage which is thus paraphrased by Hamilton. 

" In darkness — the complete obscurity of night — we 
see nothing, — there is no perception, — no discrimination 
of objects. As the light dawns, the obscurity diminishes, 
the deep and uniform sensation of darkness is modified, — 



THEIR QUALITY. 81 

we are conscious of a change, — we see something, but 
are still unable to distinguish its features, — we know not 
what it is. As the light increases, the outlines of wholes 
begin to appear, but still not with a distinctness sufficient 
to allow us to perceive them completely ; but when this 
is rendered possible, by the rising intensity of the light, 
we are then said to see clearly. We then recognize 
mountains, plains, houses, trees, animals, etc., that is, we 
discriminate these objects as wholes, as unities, from each 
other. But their parts, — the manifold of which these 
unities are the sum, — their parts still lose themselves in 
each other; they are still but indistinctly visible. At 
length, when the daylight has fiilly sprung, we are en- 
abled likewise to discriminate their parts ; we now see 
distinctly what hes around us. But still we see as yet 
only the wholes which lie proximately around us, and of 
these, only the parts which possess a certain size. The 
more distant wholes, and the smaller parts of nearer 
wholes, are still seen by us only in their conjoint result, 
only as they concur in making up that whole which is for 
us a visible minimum. Thus it is, that in the distant for- 
est, or on the distant hill, we perceive a green surface ; 
but we see not the several leaves, which in the one, nor 
the several blades of grass, which in the other, each con- 
tributes its effect to produce that amount of impression 

which our consciousness requires Clearness and 

distinctness are thus only relative. For between the ex- 
treme of obscurity and the extreme of distinctness there 
are in vision an infinity of intermediate degrees. Now, 
the same thing occurs in thought. For we may either be 
conscious only of the concept in general, or we may also 
be conscious of its various constituent attributes, or both 
the concept and its parts may be lost in themselves to con- 
sciousness, and only recognized to exist by effects which 
indirectly evidence their existence." 

4* s 



82 THE DOCTRINE OF CONCEPTS. 

The Adequacy of a Concept depends on the number 
and the relative importance of the Marks which constitute 
it, considered as more or less perfectly representing the 
objects which it denotes. A Concept may be perfectly 
Clear and perfectly Distinct, and still be a very Inadequate 
representation of the class of things for which it stands ; 
for it may connote but two or three out of the many 
attributes which they possess, and even these two or three 
may be relatively insignificant, or of trifling import as com- 
pared with several of those which ai'e omitted. The old 
Concept of man^ happily ridiculed by Aristotle, which 
described him as a two-legged animal without feathers^ is 
Clear, for it enables us easily to distinguish man from all 
other animals ; and it is Distinct, for its three Marks are 
easily distinguishable from each other ; but it is very 
Inadequate, as it omits man's crowning and peculiar at- 
tribute as a rational being. We may have a very Clear 
and Distinct Concept of an elephant^ as a quadruped that 
drinks through its nostrils; obviously, however, this is a 
very Inadequate representation of that sagacious and gi- 
gantic brute. 

The difference between the artificial system of Botany 
mvented by Linnaeus and the Natural System of Jussieu 
illustrates very well the importance of making a proper 
selection, and taking a sufiicient number, of attributes 
wherewith to determine the classes of things which w6 
think. Every plant may be perfectly distinguished from 
all other plants, and easily referred to its proper class, in 
a system founded, like that of Linnaeus, exclusively upon 
the number, situation, and connection of its stamens and 
pistils. Such a system furnishes an easy mode of as- 
certaining the names of plants, just as the alphabetical 
arrangement of words in a dictionary is the easiest way 
of enabling one to find any word that he wants. But 
the arrangement is artificial and arbitrary, the number 



THEIR QUALITY. 83 

and relative situation of the stamens and pistils in a plant 
no more determining its leading and essential cliaracter- 
istics, than the significance and mutual relations of words 
depend upon the position which their mitial letters happen 
to occupy in the alphabet. In the Natural System, these 
promment and essential attributes of plants are made to 
mark out the classes mto which they are divided, and 
thus the relations which actually exist between the things 
themselves stand out with the same relative prominence 
in the thoughts wherem they are represented to conscious- 
ness. The Concepts here not only denote their objects, 
but represent them in a manner which approximates, though 
distantly, the fulness of Intuition. 

The three merits of Clearness, Distinctness, and Ade- 
quacy, which constitute the Quality of a Concept, pre- 
suppose a reference to some standard, which, for the very 
reason that it is a standard, must be independent of our 
Thought, — that is, not subject to arbitrary change in 
Thought. Strictly speaking, every Concept considered 
merely as such, or as an individual Thought in conscious- 
ness, must have its own degree of each of these merits, 
and cannot change this degree without becoming a dif- 
ferent Concept from what it was. Whatever faults may 
be imputed to it when it is compared with some standard, 
it may still be said of it, even in its present state, that 
it connotes something and denotes something, and thus 
has all the essential characteristics which enter into our 
definition of a Concept. Any change to which it may 
be subjected is not an improvement of this Concept, but 
the substitution of another in its place, having different 
Marks, and therefore denoting not the same objects as 
before. Such a change or substitution can be required 
only through a reference in Thought to some standard, to 
which tliis Concept, or the Concept as it now stands, 
does not conform, but to which it was previously implied 
that it ought to conform. 



84 THE DOCTRINE OF CONCEPTS. 

There' are two standards, one of tlie name and the other 
of the tiling^ to one or the other of wliieh every Concept 
which the mind can form is, at least tacitly, referred. 
Words, which are the names of Concepts, are the means 
of communicating our Thought to others ; and they cannot 
perform this office unless they have the same signification 
to the hearer as to the speaker ; that is, each name must 
call up the same Concept in the minds of both. A Con- 
cept may be faulty, then, not as a Concept, (for in this 
respect, or in reference to the mere Form of Thought, 
one Concept is as good as another,) but because it has a 
wrong name, whereby it improperly assumes to be the same 
Thought which is designated by that name in the minds of 
other persons generally. Thus it is that language, among 
its other offices, has an important influence in the regula- 
tion and fixation of Thought. We do not classify things 
and form Concepts of them arbitrarily, each one accordmg 
to his own preferences; but the necessity of maintaining 
intercourse with other minds imposes on us a constant 
effort to approximate our Thoughts to theu's, — that is, 
to the Thoughts which they have fixed and established 
for general use through stamping upon them certain names. 
The Thoughts which I attach to the words church., state^ 
government, for instance, may be as correct and proper, 
in themselves considered, as the connotation which you 
attach to them ; but it is a decisive objection to my mode 
of thinking, if I attach these old and familiar names to 
peculiar combinations of Thought which they never before 
designated, and to which people generally do not now 
give these appellations. Owing to the symbolic use of 
language, in which, as already explained, words are em- 
ployed as temporary substitutes for Thoughts, we are 
continually learning and using words before we have fully 
learned their meanmg. Gradually, by a process of in- 
duction, we accommodate our use of these words to their 



THEIR QUALITY. 85 

established usage ; and it is while thus learning, that our 
Thoughts are said to be Avanting in Clearness, Distinctness, 
and Adequacy. In truth, it is not our Thoughts which 
are thus faulty, but our apprehension of other people^s 
Thoughts, or, what is the same thing, of the meaning 
which they attach to certain words. My own Concepts 
of church, state, &c. are Clear and Distinct enough, unless 
indeed I now hear these words for the first time ; but I 
cannot clearly distinguish what I imperfectly understand 
to be your Concepts of them from certain other kindred 
or nearly allied Thoughts ; or I have but an Indistinct 
knowledge of the several Marks which are connoted in 
the Concepts which you and other men have of them ; 
or my connotation of these Marks is Inadequate, — that 
is to say, not so full as other people's. 

The second standard to which our Concepts are referred, 
when they are said to be deficient in Quality, is the class 
of things which they denote, and which they consequently 
ought to represent as perfectly as possible. Thus, every 
artisan, through long use, has a more Adequate, Clear, 
and Distinct Concept of each of the tools of his trade, 
each of the objects which he works upon, and each of the 
processes to which these objects are subjected, than it is 
possible for other persons to possess who have no special 
familiarity with the business. The Concepts which these 
other persons have may be perfect enough for the correct 
use of language ; that is, they may apply the technical 
names rightly. But when compared with the full and 
accurate Notions which have been acquired by experts, 
they appear to be, as they are, very imperfect representa- 
tions of the things themselves. 

The difference between these two standards to which all 
Concepts, in respect to their Quality or degree of perfec- 
tion, are referred, enables us to understand the distinction 
wliich logicians long ago established between nominal and 



86 THE DOCTRINE OF CONCEPTS. 

real Definitions. This distinction has been very imperfectly 
apprehended by many, especially by those who, unable to 
find any other mode of distinguishing the two sorts of 
definition, have held that a Nominal one consisted only in 
explainmg the meaning of the word by synonymes, or by 
unfolding its etymology. Such a process would be Gram- 
matical rather than Logical; rightly considered, it is no 
definition at all. A Nominal Definition is the distinct 
explication of all the Marks which are connoted in the name 
of the Concept hy general consent, as evinced in the use 
of language. But language is imperfect, and words in 
common use often signify much less than exact science 
requires. A Real Definition is a distinct explication of 
all those Marks, and those only, which a careful examination 
of the class of things denoted by the word proves to be both 
Original and Essential. It is obvious that the Nominal 
and the Real Definition of a Concept will often coincide. 
This is usually the case with the technical terms in every 
science, especially those of recent origin, whose connota- 
tions are usually determined with great care before their 
names are invented. In other cases, as already explained, 
the two definitions may differ very widely ft-om each other. 
The further consideration of Definition, and of Division 
also, as the subsidiary processes by which the Quality of 
Concepts may be improved, must be postponed till after 
we have treated of 

3. The Relations or Concepts. 

The Relation of Concepts, as already remarked, is a 
technical phrase, which is understood to mean their Re- 
lations to each other only, and not to the other forms of 
Thought, which will be considered hereafter. 

A series or hierarchy of Concepts, formed by successive 
steps of Generification, like the one given in the table on 



THEIR RELATIONS. 87 

page 72, r«3presents a succession of Concepts as subordi- 
nated to each other in their two Quantities of Extension 
and Intension. But the names of the Second Intentions, 
which express the Relations of these Concepts or classes 
to each other, are given with primary reference to the 
Extension only. Unless express notice is gi^-en to the 
contrary, therefore, we shall always speak only of their 
Relation in Extension. Of any two Concepts in such a 
series, that one is called the Superior, Higher, or Broader, 
which has the greater Extension, — that is, which de- 
notes the larger number of mdividual objects ; it may 
also be called the Superordinate. The other, having less 
Extension, or denoting fewer Individuals, is called In- 
ferior, Lower, Narrower, or Subordinate. Thus, referring 
to the table again, animal is Superior or Superordinate to 
mammal, which, as included under it, or denoting fewer 
individuals, is called Inferior or Subordinate. The Supe- 
rior, also as the more general notion, and as obtained by 
the process of Generification or throwing out Marks, is 
called the Genus; while the Inferior, as more specific, and 
obtained by the process of Specification, or thinking in 
Marks, is called the Species. These names being merely 
relative, it is evident that the same Concept is, at the 
same time, a Genus to any lower Concept, and' a Species 
to any higher one. 

The Highest or Broadest Concept in such a series, 
denoting most individuals and connoting fewest Marks, is 
called the Summum Genus ; hence, it is defined by logi- 
cians to be a Genus which cannot become a Species. On 
the other hand, the lowest Concept in the sei'ies, as denot- 
ing the least and connoting the most, is called an Infima 
Species. In fact, it denotes individuals only, and not any 
classes or Species of individuals ; therefore it is defined to 
be a Species which cannot become a Genus. Each interme- 
diate Concept, as we have just said, is a Sj)ecies to those 



88 THE DOCTRINE OF CONCEPTS. 

above it, and a Genus to those below it. Its next Higher 
neighbor is called its proximate Genus ; and its next lower 
one might be termed a proximate Species, though this term 
is not in frequent use. 

When the name of any Higher Concept is applied as the 
name of a Lower one, or of an individual, it is called its 
abstract name, or its denomination in the abstract ; the pecu- 
liar or proper appellation of this lower Concept or indi- 
vidual is called its concrete name. Thus, animal is an 
Abstract, and man the Concrete, name of a rational animal; 
and again, relatively, man is the Abstract, and John the 
Concrete, appellation of the individual, this man whom we 
are speaking of. These names obviously have reference 
to the Intension of the Concept, the Abstract name being 
obtained by Abstraction, that is, by throwing out Marks, 
and the Concrete signifying all the Marks taken together 
(con-cresco^ grown together'), or the whole Intension. 

According to another and more frequent use of language, 
an " Abstract name " has a narrower signification than the 
one here indicated, being apphcable only to one peculiar 
Species of Higher Concept, instead of denoting the Abstract 
use of any Higher Concept whatever. What appears only 
as a Mark of the Concept in its Lower or Concrete use, is 
itself a Higher Concept ; and if its denotation is then 
altered, — that is, if it no longer denotes things as before, 
but only various lands and degrees of that attribute which 
the Concrete term connotes, — it is then, and then only, 
commonly called an Abstract term. Thus, to recur to tlie 
instance already given, man connoting rational animal, we 
may take rational instead of animal as the Higher Con- 
cept ; and then, altering its denotation, we may understand 
it to mean, not rational beings, but various kinds and de- 
grees of rationality. Hence, such terms as rationality^ 
redness, whiteness, humanity, &c. are called Abstract 
names. According to this use, an Abstract term is one 



THEIK RELATIONS. 



89 




which denotes that which, in its Concrete application, it con- 
noted ; it is a Mark or attribute considered as a thing. 

The Relations thus far explained, as arising from the 
higher or lower position of a Concept in the series or 
hierarchy to which it belongs, are all denominated llela- 
tions of Subordination. They may be aptly symbolized by 
a series of concentric circles, thns : — 

Here, A, having the greatest 
extent, and so containing all the 
others under it, represents the 
Summum Genus ; while F, as 
least extended, and denoting 
only individuals, not classes, 
represents the Infima Species. 
Any inteiTnediate circle, C, is a 
subaltern Genus or Species, be- 
ing Genus to D and Species to B. 
If we were to use the same diagram to symbolize the 
Relations of Intension, since the two Quantities are in 
inverse ratio to each other, the order of the letters would 
be reversed. F, as connoting the most Mai'ks or having 
the largest Intension, would be the outei'most circle, and 
A, having the least Intension, would be the innermost or 
smallest. 

In general, and for practical purposes, the terms Sum- 
mum Genus and Infima Species are applied not in an 
absolute, but only in a relati^'e sense ; — relative, that is, 
not to the totality or the smallest class of all conceivable 
things, but to the totality or the smallest convenient class of 
those things only which we are noiv thinking of ; say, all the 
objects of some particular science. Thus, in Zoology, ani- 
inal is considered as the Summum Genus, no notice being 
taken of vegetables and minerals ; and what is usually 
termed a "Variety" or " Sub- Variety " — King Charles 
Spaniel, for instance — is an Infima Species. 



90 THE DOCTRINE OF CONCEPTS. 

Absolutely speaking, logicians maintain that Summum 
Genus and Infima Species are both unattainable, • — that 
they are limits of classification in Thought, which we can 
approximate, but never reach. They express this impossi- 
bility under the form of two Laws of Thought. The first 
of these, called the Law of Homogeneity, affirms that things 
the most dissimilar must, in some respects, be similar or 
homogeneous ; and consequently, any two Concepts, how 
unlike soever, may still both be subordinated under some 
higher Concept. Thus, animals and vegetables, distinct as 
they are from each other, are both contained under the 
higher Concept organized natural objects. And even from 
this connotation, if we subtract the Mark organized, the re- 
mainder will be a still higher Concept, natural objects, which 
will include minerals, as well as a7iimal& and vegetables. 

On this ground, Mr. Mansel and other logicians main- 
tain that thing or entity, connoting but one attribute, exist- 
ence (real or imaginary), which would seem to be an 
absolute Summum Genus, is not thinkable. They deny 
that it is a possible object of Thought, on the ground seem- 
ingly that it does not contain a plurality of attributes. 
But as reasons have already been assigned (page 61) why 
a Concept, as actually thought by us, may have only one 
attribute or distinguishing Mark, I cannot see why ens is 
not thinkable, as distinguished from nihil, which has not 
even this one attribute of (real or imaginary) existence, and 
is therefore certainly not conceivable. That it is a very 
vague and indefinite Thought, is admitted ; this is a conse- 
quence of its connotation being reduced to a minimum. 
But to say, that " distinguishable from nothing " is tanta- 
mount to affirming that it is not distinguishable at all, seems 
to me in this connection, or for the purposes of pure 
Thought, a mere quibble. I can certainly think a diffijr- 
ence — that is, a relation — between being and no-being^ 
though only one term of the relation is positive, and the 



THEIR RELATIONS. 91 

otlier is merely negative. The algebraist finds a very dis- 
tinct relation between plus a and minus a, as the presence 
of one in place of the other affects the results of his calcu- 
lation very sensibly; and both these expressions are clearly 
distinguishable from zero. It is too much of a paradox to 
affirm that there is no difference in Thought between some- 
thing and nothing. 

About the second principle, called the Law of Heteroge- 
neity, there is no dispute. According to this Law, things the 
most similar must, in some respects, be dissimilar or hetero- 
geneous ; and consequently, any Concept, however large 
its Intension may be, may still have that Intension in- 
creased, without thereby descending to individuals. What 
is relatively an Infima Species, or considered as such for 
the purposes of some particular science, may be again sub- 
divided into two or more, and so on indefinitely. Thus, 
King Charles Spaniel may be subdivided into such Spaniels 
one year old^ and those of two years or older ; into those 
horn in Europe^ and those horn in America ; into those ahove^ 
and those helow, three pounds in weight, &c. Though, as 
Mr. Mansel remarks, " as far as the Laws of Thought are 
concerned, it is permitted to unite in an act of conception 
all attributes which are not contradictory of each other, it 
is impossible in practice to go beyond a very limited num- 
ber. The number of attributes in the universe not logically 
repugnant to each other is infinite ; and the mind can there- 
foi'e find no absolute limits to its downward progress in the 
formation of subordinate notions." * 

The Relation of Co-ordination exists between different 
Species which have the same Proximate Genus ; two or 
more Species are thus said to be Co-ordinate when each 
excludes the other from its own Extension, but both or all 
are included under the Extension of the same nearest 
Higher Concept. For instance, dog, wolf, cat, lion, hear^ 

* Prolegomena Logka, p. 169. 



92 THE DOCTRINE OF CONCEPTS. 

&c. are Co-ordinate Species under the same Genus, Car- 
nivora ; each excludes the other, — what is wolf is not cat^ 
— but all alike are Carnivora. As the two Quantities of a 
Concept are in inverse ratio, and as, in reference to Ex- 
tension, the Species is contained under the Genus, so, in 
reference to Intension, the Genus is contained in the Spe- 
cies. Thus, the Intension of everj Species contains the 
Genus, — that is, the aggregate of Marks wliich charac- 
terize the Genus, — and the Specific Difference, — that is, 
the aggregate of Marks by which this Species is distin- 
guished both from the Genus to which it is Subordinate, 
and from the other Species with which it is Co-ordinate. 
3Ian is a rational animal : — here, animal expresses the 
Genus to which man belongs, and rational is the Specific 
Difference whereby man is distinguished from other Species 
of animals. 

Two things may be said to be generically different^ when 
they belong to different Genera ; spedficall]/ different, when 
they belong to different Species ; individually or numeri- 
cally different^ when they do not constitute one and the 
same reality. But as every member of the hierarchy, 
except the highest and the lowest, may be viewed indif- 
ferently as either Genus or Species, generic difference and 
specific difference are only various expressions for the same 
thing. 

" Individual existences," as Krug remarks, " can only 
be perfectly discriminated by external or internal Percep- 
tion, and their numerical differences are endless ; for of 
all possible Contradictory attributes, the one or the other 
must, on the principles of Contradiction and Excluded 
Middle, be considered as belonging to each individual 
thing. On the other hand, Species and Genera may be 
pei-fectly discriminated by one or few characters. For 
example, triangle is distinguished from every Genus or 
Species of geometrical figures by the single character of 



THEIR DEFINITION AND DIVISION. 93 

trilaterality. It is, therefore, far easier adequately to de- 
scribe a Genus or Species than an Individual ; as, in the 
latter case, we must select, out of the infinite multitude 
of characters which an Individual comprises, a few of the 
most prominent, or those by which the tiling may most 
easily be recognized." We may describe, but cannot define^ 
an Individual, as there would be no end to the enumera- 
tion of its peculiar attributes. In such case, the only 
adequate definition is a view — an Intuition — of the thing 
itself. Omnis intuitiva notitia est definitio. 

The other Relations of Concepts to each other may be 
very briefly indicated. Concepts are said to intersect, 
when the Extension of one coincides in part, and only in 
part, with the Extension of the other. Thus, Frenchman 
and Protestant are Intersecting Concepts, for some French- 
men are Protestants and some are not, some Protestants 
are Frenchmen and some are not. These may be sym- 
bolized by two circles whose circumferences cut or intersect 
each other. Exclusive Concepts — animal and vegetable, 
for instance — do not coincide in any part of their Ex- 
tension, and may therefore by symbolized by two circles 
which lie wholly apart the one from the other. Recip- 
rocating^ Convertible, or Coextensive Concepts are those 
which have precisely the same Extension, as living being 
and organized being, since everything which lives is or- 
ganized. Two circles of the same diameter, and laid one 
upon the other so as to coincide throughout, would aptly 
represent Convertible Concepts. 

4. Definition and Division. 

It has already been said, that a Concept is internally 
Distinct when we can fi-illy enumerate and clearly distin- 
guish from each other all its original and essential Marks. 
The process through which this is accomplished is called 



94 THE DOCTRINE OF CONCEPTS. 

Definition. Again, a Concept is externally Distinct when 
we can fully enumerate all its subordinate Genera and 
Species. This process is called the Division of the Con- 
cept. Both processes have reference to one or the other 
of the two standards, — the name and the thing^ — bj 
which it is determined wdiether the Concept in our minds 
is, what it purports to be, a faithful copy or representation 
of what is generally designated by that name, or a full 
enumeration of the original and essential attributes of the 
class of things so designated. We will first consider 
Definition of names only. Division relating only to classes 
of things, the object of both processes being not to de- 
termine and render distinct the Concepts which we already 
possess, but to substitute others for them which shall more 
perfectly answer our purposes. The Concept to be defined 
should be called the dejiniendum, the Definition itself 
being the definientia. 

A Definition consists primarily of two parts, the Proxi- 
mate Genus and the Specific Difference of the Concept 
defined; for these two elements, as we have just seen, 
make up the whole Intension of every class. Thus, 
carnivor is a flesh-eating mammal; the word mammal here 
denotes the Proximate Genus, and flesh-eating the Specific 
Difference which distinguishes carnivora from other mam- 
mals. Such a Definition, however, is incomplete, as it is 
further necessary to define the Genus which makes a part 
of it ; and this can be done only by considering this Genus 
(mammal?) as a Species, and assigning to it its own Proxi- 
mate Genus (the next higher one in the hierarchy), ani- 
mal, and its Specific Difference, suckling its young. We 
proceed in this manner till we have reached the Summum 
Genus, each Specific Difference successively taken up be- 
ing the Mark which was abstracted in the original process 
of Generification, and the sum of these Differences being, 
therefore, the aggregate of all the Marks which make up 



THEIR -^DEFINITION AND DIVISION. 95 

the Intension of the Concept first proposed to be defined. 
What may be called the secondary or proper Definition, 
then, as before stated, is the distinct explication of all the 
Marks which are connoted in the name of the Concept. 
Thus, having successively defined dog as camivor, camivor 
as mammal, mammal as animal, and animal as thing, 
annexing in each case the corresponding Specific Differ- 
ence, we then sum up all these Specific Differences, and 
thus form the proper Definition consisting solely of these 
Differences, — that is, of all the Marks which the de- 
finiendum connotes. Hence it appears, that though the 
defining analysis is of the Intension only, yet it is regu- 
lated by the Extension, as the Extension determines the 
order in which the Intension is resolved into the Marks 
which are its elements. 

It is obvious also, that Definition by Genus and Specific 
Difference in all its successive steps supposes a previous 
knowledge of the whole hierarchy of Concepts through 
Avhich it ascends, and therefore it only explicitly enu- 
merates the Marks which were already implicitly known. 
The Classification here precedes, and is the means through 
which we fonn, the Definition. Usually, however, we 
proceed in the inverse order of this process : we seek first 
for the Definition, — that is, for a knowledge of all the 
original and essential attributes of a class of things, — as 
a preliminary step towards determining the Classification, 
or assigning the class to its proper place in a hierarchy 
of Concepts, Here, the Definition is primarily of the 
thing, and only secondarily of the name, the problem be- 
ino; how to determine the sum of the orioinal and essential 
characteristics of this class of things. The following are 
the Rules usually given by Logicians for the solution of 
this problem, — that is, for the proper formation of Defi- 
nitions. 

1. A Definition must be adequate ; that is, it must have 



96 THE DOCTRINE OF CONCEPTS. 

precisely the same Extension as the thing defined. K 
not, if the Predicate defining denotes more oljjects than the 
Subject defined, the Definition is too Wide ; if it denotes 
fewer objects, it is too Narrow. Thus, when a triangle 
is defined " a figure having tlu'ee rectilinear sides," the 
Definition is too Narrow, as there are spherical triangles 
to which it will not apply. If we say, " water is a com- 
pound of oxygen and hydrogen," the Definition is too 
Wide, as it includes not only water, but something else, — 
a deutoxide of hydrogen. When this rule is complied 
with, the Definition and the tiling defined are Reciprocat- 
ing or Convertible Concepts ; consequently, eveiything 
to which the Definition applies, and nothing to wliich it 
does not apply, is the thing defined. When this is the 
case, our Concept of this class of things has become per- 
fectly Clear, or distinguishable from all other Concepts. 
• 2. The Definition must not be tautological ; that is, it 
must not contain the name of the thing defined, as tliis 
is precisely the word wdiich we are bound to explain. It 
is equally a violation of this rule to allow any of the 
deri\atives of this name, or any of its correlative notions, 
either one of which can be explained only through the 
other, to constitute a part of the definition. This fault is 
called " defining in a circle." Lexicographers often fall 
into it unawares, as when they define a hoard to be " a thin 
plank," and then a plank to be " a thick board " ; or when 
they say that life is "vitality, the state of being ahve, 
the opposite of death." 

3. A Definition ought not to proceed by Negative or 
Disjunctive attributes, when it is possible to avoid both. 
You cannot teach me what a notion is, by merely de- 
claring what it is not, or that it is one of several tilings 
without indicating wliich one is intended. It is no real 
Definition to say of parallels, that they are " lines which 
do not meet," or of oxygen, that it is " one of the gases 



THEIR DEFINITION AND DIVISION. 97 

fit for respiration." But convenience often requires what 
Logicians call division by dichotomy, in which a Genus is 
divided into two Species having Contradictory Marks ; that 
is, one of these Species has, and the other has not, cer- 
tain well-defined characteristics, the latter, of couise, being 
capable only of Definition by negation. Thus Cuvier, 
having determined with great precision the attributes of 
Vertebrated animals, found it convenient to regard all 
other animals as Invertebrates, tliat is, as not possessing 
these attributes. 

4. A Definition must be precise, — that is, it must con- 
tain nothing unessential or superfluous. Thus, all Deriva- 
tive Marks should be excluded as superfluous, after their 
Originals have been enumerated ; for they are virtually 
contained in those Marks from which they are deducible 
by the necessary Laws of Thought, so that the mention 
of them only cumbers the Definition without really enlarg- 
ing it. That a triangle is half of a parallelogram, is no 
proper part of the Definition of a triangle, inasmuch as 
it is a necessary consequence of this figui'e having three 
sides and three angles. Unessential attributes are also 
superfluous ; that man is a featherless biped is an accident, 
not an essential trait, of his humanity. Give him a coat 
of feathers, and he is still man ; but deprive him of ration- 
ality, and he is no longer human. 

6. A Definition must be perspicuous ; for we define 
only in order to make more clear, and obscure or figurative 
expressions do not conduce to this end, but only increase 
the difficulty. " Tropes and figures," says Krug, " are log- 
ical hieroglyphics : they do not indicate the thing itself, 
but only something similar." But many expressions, origi- 
nally metaphorical, have ceased to be so through long 
use in their secondary meaning. Their original significa- 
tion has become obsolete, and no longer recurs to perplex 
us. This is the case with nearly all the words which 
6 



98 THE DOCTRINE OF CONCEPTS. 

now denote mind and its operations, though they were 
first applied only to what is material. 

Dr. Thomson takes a wider view of Definition, as in- 
cluding any Predicate which may be " usefiil to mark out 
for us more clearly the limits of the subject defined, and 
is therefore capable of being employed as a Definition for 
some thinker or other." " Any of the Predicates we 
propose to include," he continues, " though not the absolute 
Definition, not the Genus and Difference, may be em- 
ployed as a Definition by some particular person, and may 
to him fiilfil the purpose of the best logical Definition 
which can be given, " and therefore ought, if possible, 
to be comprehended under the same head." In conformity 
with this view, he enumerates the following six sources 
from which convenient Definitions may arise. 

"i. From Resolution, when the Marks of the definitum 
are made its definition ; as in ' a pension is an allowance 
for past services.' It is not necessary that the Marks 
should be completely enumerated, — that the conception 
should be strictly adequate, — but only that the Marks 
should suffice for the identification of the Subject, as belong- 
ing to it all and to it alone ; so that Aristotle's Property 
would be included in it. ii. From Composition, the reverse 
of the last method, in which the definitum, a conception of 
which the component Marks are enumerated, stands Subject 
to a Definition implicitly containing those Marks ; as, 'those 
who encroach upon the property of others are dishonest.' 
iii. From Division, where we define the Subject by enumer- 
atino; its Dividing Members : as, ' Britons are those who 
dwell in England, Scotland, or Wales.' All the jvidg- 
ments called disjunctives are under this head. iv. From 
Colligation, the exact reverse of the last ; where the Divid- 
in<T Members of a conception are enumerated in the Subject, 
and the divided conception itself added to define them ; as, 
'historical, philosophical, and mathematical sciences are the 



TUKIR DEFINITION AND DIVISION. 



99 



sum (i. e. are all, or equal) of human knowledge.' This 
is the form which Inductive Judgments naturally assume. 
V. From change of Symbol, where both Subject and Predi- 
cate are symbolic conceptions, the latter being given as a 
substitute for the former on a principle of expedience only ; 
as, ' probity is honesty.' This is the nominal definition of 
some logic-books, vi. Fron^ Casual Substitution, where 
one representation is put for another on a principle of 
expedience only, as serving to recall the Marks, which 
both possess in common, more readily to the hearer's 
mind ; as, ' the science of politics is the best road to suc- 
cess in life ; pleasure is the opposite of pain.' 
" Table of Definition. 



d 
.2 i 



By its In- 
tension (or 
Mar'vs) 

By its Ex- 
tension (or 
Sphere) 

By Acci- 
dental Co- 
incidence 



being unfolded, = i. 

being reunited, = ii. 
being divided, = iii 



Kesolution, or 
Definition 
proper. 
Composition. 

Division. 



being reunited, = iv. Colligation. 

of a Symbol, = v. Nominal Defi- 
nition. 

of Notation, = vi. Accidental Defi- 
nition." 



As absolute Definition resolves the Intension of a Con- 
cept into its constituent Marks, so Division resolves the 
Extension into its constituent Genera and Species. In its 
most general acceptation, division is the separation of any 
whole into its parts. But Logical Division, with wliich 
alone we are here concerned, is such a separation of a Logi- 
cal Whole only, — that is, of a class containing tmder it other 
classes, which are regarded as its parts. An individual 
is so called (in-divido) because it cannot be (logically) 
divided ; the process of cutting it apart is properly called 
Partition, not Division. The Mathematical or Integral 
whole is such an individual, and can be sundered into its 



100 THE DOCTRINE OF CONCEPTS. 

parts only by Partition. The parts of an Essential or 
Physical Avhole, as they interpenetrate and inform each 
other, cannot be separated at all except in Thought. But 
a Logical whole is itself a creation of Thought, formed 
out of lesser wholes of the same kind, into which it can 
be resolved by mental analysis. 

By Partition, triangle may ^e resolved into smaller tri- 
angles, or into angles and sides ; the former Partition may 
be actual, while the latter can only be ideal, — that is, it 
is possible only in Thought. By Division, on the other 
hand, triangle is resolved into rectilinear and curvilinear 
triangles, or into equilateral, isosceles, and scalene triangles, 
as these are Species comprehended under one Genus. 

The Genus to be divided is called the divisum, and 
the constituent Species into which it is resolved are the 
dividing members (membra dividentia'). Agreeably to the 
nature of a hierarchy of Concepts, the parts which result 
from such a Division are in themselves wholes containing 
other parts under them, and the dividing process repeated 
upon these is called a Subdivision. The same Concept 
may likewise be differently divided from different points 
of view, each separate analysis proceeding on what is 
technically termed its own fundamentum divisionis, or 
peculiar Ground of Division. Thus, man may be divided 
geographically into European, Asiatic, American, &c. ; or, 
in reference to color, into white, red, and blach men ; or, 
in reference to religion, into Christians, Mohammedans, and 
Pagans; — local position, color, and religion being here 
the successive fundamenta divisionis. So the books in 
a library may be arranged either according to size, as 
folios, quartos, octavos, &c. ; or according to the languages 
in which they are written, as Latin, French, English, 
&c. ; or according to the subjects of which they treat, as 
theological, scientific, historical, &c. Perhaps the most 
important point in the philosophy of the Classificatory 



THEIR DEFINITION AND DIVISION. 101 

Sciences is the right selection of a fundamentum divisionisj 
or Ground of Division. 

If a Division has only two parts or members, it is called 
a dichotomy ; and if such a Dichotomy is exhaustive, as it 
should be, these two members are evidently Contradictories 
of each other ; for whatever is contained in one is thereby 
excluded from the other, and the two, taken together, 
constitute the whole. Accordingly, these two Dividing 
Members can always be expressed under the formula B 
and not-B. Thus, in dividing triangle, instead of calling 
the two members rectilinear and curvilinear, it is better 
to denominate them rectilinear and non-rectilinear. A 
Division into three members may be called a trichotomy ; 
into many, a polytomy. 

Logicians have commonly given the following Rules for 
the proper Division of a Concept. 

1. Each Division should have but one fundamentum 
divisionis, by which every part of the process is regulated. 
The intervention of more than one Ground of Division 
in the same process is the Logical fault which is called a 
Cross Division. Thus, a Division of man into European, 
American, Negro, and Pagan is faulty, because the Ground 
of Division for the first two Dividing Members is local 
position; for the third, it is color ; and for the fourth, it 
is religion. The consequence of this blunder is, that the 
same individual might be contained in each of the last 
three Members ; — for he may be at once American, Negro, 
and Pagan. Whatever we may select as a Ground of 
Division, it must evidently be a Mark or attribute of the 
Divisum, and the number of distinct forms or varieties, 
under which this attribute appears in the class of things 
to be divided, will determine the number of Dividing 
Members. One of the Dividing Members, however, and 
but one, may be marked only by the absence of this 
attribute. 



102 THE DOCTRINE OF CONCEPTS. 

2. The Mark selected as the Ground of Division should 
be an Essential attribute of the Divisum, and one which 
has as many Derivatives, or which determines as many 
of its other attributes, as possible ; otherAvise, the Division 
will be complex and purposeless. Thus, the color of the 
hair is an unessential attribute of man ; mankind might 
be divided into a large number of classes in this respect, 
but as very few of his physical, and none of the intellectual 
or moral, qualities of a man can be inferred from the fact 
that he has red, brown, or black hair, the Division would 
be useless. On the other hand, a classification of men 
according to their nationality or race, their geographical 
position, or their religion, is found to be an eminently 
fruitful one, as many of their other attributes are fomid 
in invariable connection with these leading characteristics, 
so as to be readily determined by them. The purpose 
for which a Division is made often determines the selection 
of its Ground. Thus, soldiers may be conveniently divided 
into cavalry and infantry^ as this distinction is one of great 
moment in military affairs ; but to divide men in general 
into foot and horsemen would be absurd. 

3. No Dividing Member must by itself exhaust the 
Divisum ; and the Dividing Members, taken together, 
must exhaust, and no more than exhaust, the Divisum. 
As the Genus and the Co-ordinate Species into which it 
is divided stand to each other in the relation of a whole 
to its parts, the propriety of this rule is manifest. Man 
cannot be divided into rational and irrational, for the one 
class of rational beings includes all men, so that neither 
of the Dividing Members is a part, or the result of a 
Division, properly so called. Again, as all the parts are 
required to constitute a whole, if the Co-ordinate Species, 
taken together, do not exhaust the Genus, the Division is 
obviously imperfect ; one or more members remain to be 
supplied. If, on the other hand, they overlap the Genus, 



THEIR DEFINITION AND DIVISION. 103 

there is somewhere an excess, which ought to be sub- 
tracted and referred to another class. Government cannot 
be divided into monarchical^ aristocratic, and deraocratic ; 
as there is a fourth class, the mixed. The old Division 
of the science of language into Grammar, Logic, and 
Rhetoric is redundant, as Logic is concerned with the 
laws of thought rather than of utterance, and therefore 
properly belongs to the science of mind. 

4. The Co-ordinate Species into which a Genus is di- 
vided must be reciprocally exclusive; that is, no one of 
them must, in whole or in part, contain any other. In 
order to ascertain whether this rule, the propriety of 
which is obvious, has been complied with. Logicians apply 
the test of Dichotomy, to which any other Division, how- 
ever complex, may be reduced. Thus, all the Co-ordinate 
Species, B, C, D, E, &c., of any Genus, A, may be rep- 
resented under any one of the formulas, B and not-B ; G and 
not-C ; D and not-D, &c. If the Dividing Members are 
mutually exclusive, C, D, and E will each be found under 
not-B ; B, D, and E, under not-C; B, C, and E, under 
not-B ; and so on. This rule is violated in a Cross Divis- 
ion, where, as we have already seen, the same individuals 
may appear under two or more of the Dividing Members : 
and also when a Member of a Subdivision is improperly 
co-ordinated with the Members of a primary Division. 
This last fault, however, is properly ranked under the next 
following rule. The ten Categories of Aristotle are now 
generally condemned as a faulty Division, because the 
last six of them are only subdivisions of the fourth, Relation. 
" For the Category where is the relation of a thing to 
other things in space ; the category when is the relation 
of a thing to other things in time ; action and passion 
constitute a single relation, — that of agent and patient" ; 
&c. 

5. A Division must proceed step by step, in regular 



104 THE DOCTEINE OF CONCEPTS. 

order, from proximate to remote differences, not over- 
leai)ing any step which is properly intermediate. In other 
words, eacli Species, as it appeal's among the Dividing 
Members, must emerge directly from the Division of its 
own Proximate Genus. Divisio ne fiat per saltum vel hia- 
tum. Even the ordinary Division of all natural objects 
into animals, vegetables, and minerals is faulty in this re- 
spect, its three Species not being properly co-ordinate, as 
one step has been omitted. The primary Division should 
be by Dichotomy into organic and inorganic things, animals 
and vegetables appearing subsequently as a subdivision of 
the organic. 



THE DOCTRINE OF JUDGMENTS. 105 



CHAPTER V. 



THE DOCTRINE OF JUDGMENTS. 



1. The Predicables and the Categories. — 2. The Quantity, Quality, and Re- 
lation of Judgments according to tlie Aristotelical Doctrine. — 3. Tlie 
Hamiltonian Doctrine of Judgments. — 4. The Explication of Propo- 
sitions into Judgments. 

JUDGMENT is that act of mind whereby the rela- 
tion of one Concept to another, or of an individual 
thing to a Concept, is determined, and, as a consequence 
of such determination, that two Concepts, or the individual 
thing and the Concept, are reduced to unity in Thought. 
A Judgment expressed in words is a Proposition, the 
two terms of the Judgment being called the Subject and 
Predicate of the Proposition. The assertions, iron is mal- 
leable, John is brave, determine a relation of agreement 
between the two terms involved in each, whereby these 
two are conceived as one, and thus expressed, malleable 
iron, brave John. On the other hand, the Judgment, 
quadrupeds are not rational, determines the relation of 
disagreement between the two Terms, so that one is now 
denied to be a Mark of the other, or, what is the same 
thing, the negative Mark, irrational, is now attached to 
the Concept, quadruped. 

As we have already defined a Concept to be a repre- 
sentation of one or more objects through their distinctive 
Marks, it is evident that Judgment is the process through 
which Concepts are formed. In fact, to judge is to recog- 
nize a particular Mark or attribute as belonging, or not 

5* 



106 THE DOCTRINE OF JUDGMENTS. 

belonging, to a certain object or class of objects. The 
Judgment is not, strictly speaking, a comparison, but it 
is the mental act of conjoining or disjoining two things 
which results from a previous comparison of them with 
each other, and a consequent recognition of their agree- 
ment or disagreement. Hence, as Hamilton remarks, 
"every Concept is a Judgment fixed and ratified in a 
sign " ; and, again, " a Concept may be viewed as an 
implicit or undeveloped Judgment ; a Judgment as an 
explicit and developed Concept." Thus, the Concept 
man, which has the four Marks biped, two-handed, rational, 
animal, is the combined result of four separate Judgments 
which affirmed each of these attributes to be characteristic 
of man. Aristotle, the Father of Logic, seems to have 
regarded Judgments as the primary elements, out of 
which Concepts are formed ; for his whole system is based 
upon an analysis of Judgments. Modern writers have pre- 
ferred, as more convenient, and at least equally correct, 
the view which has here been taken, that Concepts are 
the elements of Judgments. In truth, each presupposes 
the other. If it be asked which, in the order of the 
mind's development, comes first, the answer is, neither; 
but a partial and confiised apprehension of a thing, which 
is a young child's substitute for a Concept, and which is 
first cleared up by a succession of Judgments producing 
Concepts properly so called. Judgment is not arbitrary 
or dependent upon the will ; I must, in Tliouglit, affirm 
the union or the separation of the two Terms, according 
as the relation of agreement or disagreement is perceived 
to exist between them. Hence, the Judgment is always, 
at least subjectively, true ; the Proposition, which is only 
the verbal affirmation, may be either true or false, accord- 
ing as it does, or does not, agree with the mental Judgment. 
The mere succession or coexistence of two Thoughts in 
the mind does not constitute a Judgment. I may think 



THE DOCTRINE OF JUDGMENTS. 107 

first of man, and then of animal ; but no Judgment takes 
place until I affinn in Thought a perceived relation between 
them, — until I think man is animal. Such a relation can- 
not be perceived between them unless one is regarded as 
an attribute or determination of the other ; — that is, one 
must be regarded as determining, and the other as deter- 
mined. For if both were viewed as determining, there 
would be nothing determined ; and both cannot be deter- 
mined, unless there is something determining them. Hence 
there are three necessary parts of a Judgment ; — first, the 
Concept or thing determined, which is called the Subject ; 
secondly, the determming or attributive notion, which is 
called the Predicate; and, thu-dly, that which expresses 
the relation of determination betAveen the Subject and the 
Predicate is called the Co'pula. The Subject and Predicate 
are called the Terms (termini^ or Extremes of the Judg- 
ment ; and the Copula may therefore be symbolized as a 
straight line connecting the two points which are its Terms 
or ends. 

Though a Judgment necessarily consists of two Terms, 
it is nevertheless a single act of mind. There is a separate 
act of mind, whereby I perceive or conceive each of the two 
Terms taken sepai*ately ; but it is only one act by which I 
perceive and affirm the relation between these two Terms, 
and thereby unite them into one process of Thought. 

When the mental Judgment comes to be expressed in 
words as a Proposition, each of its three parts does not 
necessarily appear as a distinct word. The idiom of lan- 
guage often requires or enables us to express two, or even 
all three, of them by a single word ; but, in accordance 
with the general Postulate of Logic, that we must be al- 
lowed to express all that is imphcitly thought, we cannot 
deal logically with the Proposition until its form is so modi- 
fied as to allow all the three elements to appear separately. 
Moreover, as has been already remarked, the Copula of a 



108 THE DOCTRINE OF JUDGMENTS. 

Judgment, since it expresses the present union of two 
thoughts now before the mind, must always appear as the 
present tense of a verb, — usually of the verb to be : is or 
IS NOT is commonly regarded as the only distinctive expres- 
sion of the logical Copula. Thus the Propositions, the sun 
shines ; pluit ; cogito, ergo sum ; he came yesterday ; John 
will arrive ; if reduced to their logical form as Judgments, 
must be thus expressed: the sun is shining ; the rain is 
falling; I am thinking, therefore I am existing ; he is the 
person who came yesterday ; John is he who will arrive. In 
each of these cases, all that precedes the Copula, is or am, 
is the Subject, and all that follows the Copula is the Predi- 
cate.* The substantive verb, when used as a Copula, 

* Hence we perceive how unfounded is the objection which has been made 
to the science of Formal Logic, on the ground that it does not expound the 
whole theory of reasoning, because it furnishes no explanation of an infer- 
ence so obvious as this : — 

A is greater than B ; 
therefore, B is less than A. 

But here ihe Predicate is not B or A, but " greater than B " and " less than 
A " ; the meaning of these two expressions, therefore, belongs to the Matter 
of Thought, with which, as a logician, I have nothing more to do than with 
the meaning of A or B taken alone. That these two expressions have a 
correlative meaning, is a fact which belongs to the science of language rather 
than to that of Thought. Instead of regarding one of them as an inference 
from the other, it would be more correct to say that the two are equivalent 
statements of the same fact ; they express one relation between two Con- 
cepts. That two lines converge from A to B is only another way of saying 
that the same two lines diverge from B to A ; there is but one thing to be 
said, though there are two modes of saying it. In liise manner, we may say, 
but we do not argue, that 

Socrates is the husband of Xantippe ; 
therefore, Xantippe is the wife of Socrates. 

God alone is omnipotent ; 

therefore, no one is omnipotent but God. 

In such cases, the second proposition is an interpretation of the preceding 
one, not an inference from it. Wo learn from a dictionary, not from a 
treatise on Logic, what different phrases are equivalent statements of one 
and the same Thought. 



THE DOCTRINE OF JUDGMENTS. 109 

never means exists ; but the idea of existence^ when it Is 
intended to be conveyed, forms the Predicate. He is, in 
the sense of he exists, is logically interpreted, he is existing. 
Fuit Ilium ; Troy is that which has been, — is that which 
exists no longer. 

Logicians generally maintain that the Copula is precisely 
equivalent to the mathematical sign of equality. In many 
cases, this is undoubtedly true. If the Predicate is simply 
a definition of the Subject, or if the Proposition in any 
manner expresses the entire equivalence of its two Terms, 
it can then be expressed in the manner of an equation. 
Thus, Saltpetre = nitrate of Potash ; Alexander = the son 
of Philip. But the two Terms of a Judgment are not 
always convertible or equivalent. What is thought and 
expressed is always a relation between the two Terms, but 
is not always a relation of equivalence or identity. Some- 
times, as in a negative Judgment, it is a relation of disa- 
greement ; sometimes the Predicate expresses merely one 
attribute of the Subject, and then the relation is that of a 
whole to its part, since only a portion of the Subject's In- 
tension is affirmed of the Subject. When we say, the apple 
is red, we do not mean apple = red, but only that a red 
color is one out of many attributes of the apple, — is a part 
of its Intension. In this case, the Copula signifies rather 
possession, to have, than equality, to be. The form of the 
Judgment as thought is, the apple has a red color as one of 
its many attributes. 

It is e^ddent, then, that there are two classes of Judg- 
ments, properly distinguished by Dr. Thomson as Substitu- 
tive and Attributive. In Substitutive Judgments, the sign 
of equality may be used as the Copula ; the Predicate is 
properly identified with the Subject, or made convertible 
with it, and therefore every attribute of the one may also 
be affirmed of the other. If A = B, then every a; of A 
is also a; of B ; all that is true of "Alexander" is also true 



110 THE DOCTRINE OF JUDGMENTS. 

of " the son of Philip." But if the Judgment is only At- 
tributive, the sign of equality cannot be used ; the two 
Terms are not convertible, and consequently it cannot be 
inferred that they possess the same attributes. Sweetness 
or sourness is a quality of the apple, but not of the red 
color which belongs to the apple. 

The distinction here explained is a vahd and important 
one in respect to Judgments considered simply as such, or 
as mere phenomena of Thought, irrespective of any use to 
be subsequently made of them in reasoning or other mental 
processes. In Attributive Judgments, the Predicate is 
actually thought only connotatively, as a Mark or attribute 
of the Subject, and not denotatively, as the name of a class 
of things. And hence Mr. Mill is led to maintain, that 
such Judgments never express truths of classification, and, 
therefore, that the generally received doctrine of Predica- 
tion, that it consists in placing something in a class or ex- 
cluding something from a class, is entirely unfounded. 
" When I say that snow is white,^^ he argues, " I may and 
ought to be thinking of snow as a class ; but I am certainly 
not thinking of white objects as a class ; I am thinking of 
no white object whatever except snow^ but only of that, and 
of the sensation of white which it gives me." 

All this is granted. At the moment of forming the Judg- 
ment, white is not consciously before the mind as the name 
of a class of things. We then think of it only connotatively, 
— only as a Mark. But it is still time that we originally 
learned the meaning of the word white not only as a Mark 
connoting a quality, but also as a Concept denoting a class 
of things, — namely, white objects ; otherwise, it would not 
be, what it certainly is, a Common Name of snow, milk, 
chalk, and many other things. And though this its deno- 
tative meaning — its Extension — is not consciously before 
the mind when it is used as a Mark or as a Predicate, it is 
still there potentially, and must be brought out or expressed 



THE DOCTRINE OF JUDGMENTS. Ill 

•when we attempt to found an inference upon this Judg- 
ment, or to employ it as one of the premises in a syllogism. 
To borrow Mr. Mill's own instance, — if I am in doubt 
whether Chimborazo is snow-covered, I may reason 
thus : — 

All mountains of a certain altitude, and whose summits 
are perpetually white, are snow-covered. 

But Chimborazo's lofty summit is always white, — that 
is, it is one of this class of mountains. 

Therefore, Chimborazo is snow-covered. 

As already observed (p. 64), "the distinction between 
Concepts and Marks is not absolute, but relative; they 
may be used interchangeably." That a Concept or Com- 
mon Name is sometimes used only as a Mark, or with no 
conscious reference at the moment to its denotation, is 
surely no proof that it is always so used, or even that the 
denotative meaning, or Extension, is not potentially present 
in this very case, so that it may be revived, if need be, 
and an inference founded upon it. Because words are 
sometimes used symbolically, or without spreading out in 
Thought all their signification, it does not follow that they 
are always so used, or that such use of them may not be 
checked, and kept from falling into error, by occasionally 
bringing up into consciousness what they always potentially 
signify in Thought. It follows, then, that although a Judg- 
ment, as actually thought, ''^^^J ^^^ he a truth of classification, 
and therefore that the Copula may not be equivalent to the 
mathematical sign of equality, yet it may always be reduced 
to the form of such a truth, and then this mathematical 
sign fully expresses its proper form; and in reasoning, 
such a reduction is generally necessary. Though it is not 
true that apple = red, it is true that apples = some red 
objects ; or, as it is more commonly expressed Jby Conver- 
sion, some red objects are apples. 



ijun 

Tninl 



112 THE DOCTRINE OF JUDGMENTS. 

1. The Peedicables and the Categokies. 

In his analysis of Judgments, Aristotle was led to con- 
sider how many kinds of Predicates there are, when 
viewed relatively to their Subjects ; — in other words, to 
determine the Second Intentions of Predicates considered 
in relation to Subjects. Thus was formed his celebrated 
doctrine of the Predicables, — a doctrine which was con- 
siderably modified, but not improved, by his followers, 
Porphyry and the Schoolmen. According to Aristotle, 
every Judgment affirms or denies one of four relations of 
a Predicate to its Subject. It expresses either, — 1. the 
Genus.) i. e. the class under which it is included, as when 
we say, man is an animal; or, 2. the Definition, which, 
as we have seen, is the Genus and the Specific Difference 
taken together, and may be reduced to an enumeration 
of all the essential Marks of the Subject, as, a Carnivor 
is a flesh-eating Mainmal ; or, 3. a Property, that is, some 
peculiar attribute of the Subject, belonging to it univer- 
sally, belonging to nothing else, and yet not regarded as 
essential to it, for we could conceive of the thing without 
it, — as polarity is a Property (proprium') of the magnet., 
and risibility of man; or, 4. an Accident, which is an 
attribute that happens to belong to the Subject, but, as 
unessential, is separable from it, as man is learned. 

Two of these Predicables, namely, the Definition and 
the Property, are convertible with the Subject, or may 
change places with it ; and of these two, the former ex- 
presses the whole Essence (all the essential qualities), while 
the latter, strictly speaking, is no part of the Essence ; for 
we can conceive of man as not having the attribute of 
risibility, but we cannot conceive of him as deprived of 
rationality. 9 So, the magnet can be conceived of without 
polarity, as its magnetic or attractive power was known 
long before its property of pointing to the north was dis- 



THE PREDICABLES AND THE CATEGORIES. 113 

covered ; but its magnetic or attractive quality is essential 
to our conception of it. Of the two other Predicables, 
Genus and Accident, neither is convertible with the Sub- 
ject ; and, again, the former expresses a part of the Essence, 
and the latter does not. Thus we have the following 
scheme of the Predicables: — 

Definitioa expressing the whole Essence > convertible 

Property expressing no part of the Essence ) with the Subject. 

Genus expressing a part of the Essence ) inconvertible 

Accident expressing no part of the Essence ) with the Subject. 

Porphyry and the Schoolmen modified this analysis, but 
did not improve it, in their attempt to make it conform 
to their philosophical doctrine of Realism. The Realists 
maintained, that Univei'sals or Species are not mere classes 
of things arbitrarily formed by the mind, but are real exist- 
ences, with perfectly well-defined limits, existing in things, 
and yet independently of them and of our conceptions 
of them. Each Universal is the common and essential 
element — the Essence — of all the individual things which 
are included under it and denoted by its Name. What- 
ever other attributes these individuals possess do not belong 
to their Essence, but are considered as their Properties 
or Accidents. According to this view. Species has a de- 
terminate and fixed meaning, corresponding very nearly 
to what we have termed the Infima Species ; it was 
absolutely the lowest class to which anything can be re- 
ferred, and not merely the lowest relatively, as we have 
defined it. Every Specific Difference, moreover, signifies 
absolutely the attribute whereby a given Species is dis- 
tinguished fi'om every other Species of the same Genus. 
Both Species and Genus are thus supposed to be absolutely 
determined, following the patterns or archetypes of them 
which exist in the Divine Mind, and which presided over 
their creation, instead of being mere creatures of our 
Thought, and springing from arbitrary classifications, ac- 

H 



I 



114 THE DOCTRINE OF JUDGMENTS. 

cording to which the same individual may be referred to 
any one of several different Species, and again the same 
Species to one Genus or another, according as it suits our 
purpose. The Realists mamtained that the hierarchy of 
classification is not fluctuating and arbitrary, formed by 
man for his own convenience, and therefore always chang- 
ing to suit his ever-varying purposes ; but they held that 
it resulted from the real nature of things, as determined 
by the Creator, and therefore is a perfect and immutable 
copy of the Divine Thought. To adopt Mr. Mill's lan- 
guage, " they did not admit every class which could be 
divided into other classes to be a Genus, or every class 
which could be included in a larger class to be a Species. 
Animal was by them considered a Genus; and man and 
brute^ co-ordinate Species under that Genus : biped would 
not have been admitted to be a Genus with reference to 
man, but a proprium or accidens only. It was requisite, 
according to their theory, that Genus and Species should 
be of the Essence of the Subject. Animal was of the 
Essence of man; biped was not. And in every classifi- 
cation, they considered some one class as the lowest or 
Infima Species ; man, for instance, was a lowest Species. 
Any other divisions into which the class might be capa- 
ble of being frirther broken down, as man into white, black, 
and red man, or into priest and layman, they did not 
admit to be Species." They wrongly assumed, — 1. that 
the Divine Mind classifies at all (see p. 15) ; 2. that it 
would be possible for man to follow the thought of the 
Creator so far as to copy without error such classification, 
even if it existed ; 3. that there is no occasion, even for 
purposes of human science and convenience, to distribute 
the same mdividual things into different systems of clas- 
sification, assuming various Grounds of Division, according 
to the special ends in view. 

Adopting the Realist hypothesis, the Schoolmen distin- 



THE PREDICABLES AND THE CATEGORIES. 115 

guished these five Predicables, — Gemis, Species, Differ- 
ence, Property, and Accident. Comparing this hst with 
that of Aristotle, we perceive that Definition is omitted, 
— being resolved into its two elements, Genus and Specific 
Difference, both of which are admitted into this scheme, — 
and that Species also is added. The Species here intended 
is the Infima Species, or proximate class, and is usually de- 
fined as being the whole Essence of the individuals of 
which it is predicated. Difference is also taken abso- 
lutely, being regarded as predicable of this class and of 
none other, — that is, as serAang to distinguish this Species, 
not merely fi.'om the other Species in the same Genus, but 
fi'om all others whatever. Aristotle omitted Difference 
fi'om his list, because, as he says, it is " of the nature of 
Genus," or, as we should say, it is interchangeable with 
Genus. In truth, each of the two elements of a Definition 
is a Genus ; they are two communicant or overlapping 
Genera. But it is more convenient to regard one as de- 
termined, and the other as determining, — that is, one as 
Genus and the other as Difference. Thus, man is a ra- 
tional animal; here are two Genera, rational hehigs and 
animal beings, which partially include, and partially ex- 
clude, each other. As there are some rational beings 
which are not animal (^angels, for instance), so there are 
some animals (^brutes') which are not rational ; but man is 
both animal and rational, — that is, he is the common part 
of the two overlapping Genera. He is, therefore, a rational 
animal being, or, what is precisely the same thing, he is an 
animalized rational being. In the former case, animal is the 
Genus and rational is the Specific Difference ; in the latter 
ease, this is reversed, rational 
being the Genus and animal 
the Difference. Thus : — 
Let A = animal ; 
B = rational ; 
then, C = rational animal. 




116 THE DOCTRINE OF JUDGMENTS. 

Aristotle evidently perceived, vv^hat his followers did not, 
that there is no real distinction between Genus and Differ- 
ence ; that both of them are, in truth, Genera ; and hence 
that Difference, being of the nature of Genus, cannot be 
admitted into the list of distinct Predicables. 

Having ascertained the Second Intentions of Predicates, 
which are the Predicables, Aristotle attempted to carry the 
analysis of Judgments one step farther, by determining their 
First Intentions, and was thus led to foim his celebrated 
list of the ten Categories or Predicaments. In other words, 
having determined how many sorts of Predicates there are 
in relation to their Subjects, he next inquired Jiow many 
and what particular things may be predicated of any Sub- 
ject. Considering every Judgment as the answer to a 
question, he sought to ascertain how many and what dif- 
ferent questions maybe asked concerning a Subject, — what 
are the several determinations of which it is capable. The 
inquiry evidently concerns the Matter, and not the Fonn, 
of Thought, and therefore does not properly faU within the 
province of Logic, which is exclusively occupied with Sec- 
ond Intentions. But the Categories may be regarded as a 
curiosity in the history of the science, and as a monument 
of the genius of its founder for abstract thought and com- 
prehensive generalization. Great ingenuity has been 
wasted upon the discussion of them by his followers. For 
many centuries, during which the boundaries of the science 
were not so strictly defined as they now are, the doctrine 
of the Categories occupied a prominent place in every 
treatise upon Logic. A very brief explanation of it Avill 
answer our present wants. 

The Greek verb from which category is derived properly 
signifies to accuse^ or to affirm something of any one, and 
hence, to predicate. But the noun has been diverted by 
logicians fi'om signifying affironation or predication, and 
applied to a list or class of things of the same Jcind which 
may he predicated of any Subject. Aristotle affirms that 



THE PREDICABLES AND THE CATEGORIES. 117 

there are ten Categories, or classes of tilings tliat may be so 
predicated, — namely, 1. Substance; 2. Quantity; 3. Qual- 
ity; 4. Relation ; 5. Place ; 6. Time ; 7. Postui'e ; 8. Pos- 
session ; 9. Action ; 10. Passion. According to a fashion 
very common among the Scholastic logicians, of manufac- 
tuiing Latin verses as aids to the memory m retaining the 
technicalities of the science, the several Categories are in- 
dicated in the two following lines, though in a somewhat 
different order from that given above, as shown by the 
numerals prefixed. 

12 3 4 9 10 

Arbor sex servos fervore refrigerat ustos ; 

5 6 7 8 

Euri eras stabo, nee tunicatus ero. 

The four Predicables, argues Aristotle, — "the Accident, 
the Genus, the Property, and the Definition, — will always 
be in one of these Categories [or classes] ; since, through 
these, all propositions signify either what the Subject is, or 
how much it is, or what sort of a thing it is, or some one of 
the other Categoi-ies " ; as, what relation it hears to some 
other thing, or its place^ its time^ its posture, what it has, 
or does, or suffers. Adopting Aristotle's OAvn examples of 
predication under each of these classes, we may, for in- 
stance, affirm of anything, — 1. under the Category of 
Substance, that it is a man, a horse, or the like ; 2. under 
that of Quantity, that it is two cubits long, three cubits, 
&c. ; 3. under that of Quality, that it is white, grammat- 
ical, &c. ; 4. under that of Relation, that it is double, half 
as large, greater, &c. ; 5. under that of Place, in the 
Lyceum, in the Forum, &c. ; 6. under that of Time, yes- 
terday, last year, &c. ; 7. under Posture, standing, seated, 
&c. ; * 8. under Possession, having shoes or armor, &c. ; 

* Many Avriters have interpreted Aristotle's seventh Category, KelcrBai., as 
Situation. But, as Situation is identical with Place, this interpretation makes 
the seventh redundant and unnecessary. Besides, the examples here selected 
prove that Aristotle here understands KeladuL to signify Posture. 



118 THE DOCTRINE OF JUDGMENTS. 

9. under Action, it cuts^ burns, &c. ; 10. under Passion, 
it is cut, is humed, &c. 

The purpose of Aristotle in fi'aming his scheme of the 
Categories, and the nature of the Categories themselves, 
have been very differently understood by different writers, 
who, in commenting upon them, seem to have had much 
more reference to their own systems of metaphysical phi- 
losophy than to a fair interpretation of the text of their 
author. Thus, Kant assumes that Aristotle's intention was 
to form a complete list of the a priori conceptions of the 
intellect, or of the forms which the mind imposes upon 
things by its own mode of thinking them. Under this m- 
terpretation, he asserts very tinily, that the analysis is not 
formed upon any one principle ; that the enumeration is 
incomplete ; that empirical notions are intruded among the 
pure, and derivative among those which are original. 

Mr. Mill supposes that the Categories are " an enumera- 
tion of all things capable of being named, — an enumera- 
tion by the summa genera; that is, the most extensive 
classes into which things could be distributed ; which, 
therefore, were so many liighest Predicates, one or other 
of which was supposed capable of* being affirmed with 
truth of every namable thing whatsoever." Taken in 
this light, he finds, of course, that the list is both redun- 
dant and defective ; that Relation includes Action, Passion, 
and several others ; and that " mental states," wliich, in 
Mr. Mill's opinion, are neither substances nor attributes, 
are omitted entirely. 

Sir William Hamilton's interj:)retation of the Categories 
agi'ees very nearly with that of Mr. Mill. He finds that 
they are an enumeration of the highest genera of Being 
or Existence, — that is, of all things whatsoever ; and, 
under this view, justly objects that Being ought first to be 
divided by dichotomy, into absolute and relative Being, 
the first of which coincides with Aristotle's first Category, 



THE PREDICABLES AND THE CATEGORIES. 119 

that of Substance, while the second includes the other 
nine : and that the last six may all be reduced to the 
fourth, that of Relation. 

Trendelenburg, who is followed by Mr. Mansel, main- 
tains that the Categories are, to adopt the language of the 
latter, " an enumeration of the different modes of naming 
things, classified primarily according to the grammatical 
distinctions of speech, and gained, not from the obsei'vation 
of objects, but from the analysis of assertions." This 
doctrine seems to be correct ; but it is obviously irrelevant, 
for it explains only the genesis, not the nature, of the 
Categories. To show the source of the classification, or 
how Aristotle was led to make it, is very different fi'om 
explaining the natvu'e of the things classified, and the real 
distinctions between the several classes. 

And the ground for the other criticisms falls away when 
it is considered, that the distinction between the Form and 
the Matter of Thought — that is, between Logic and 
Metaphysics — is but very imperfectly preserved by Aris- 
totle. But although much of what properly belongs to 
Metaphysics is intruded into his treatises upon Logic, and 
vice versa, it is never considered there primarily in its 
metaphysical nature, but only in its logical relations. The 
doctrine of the Categories, as conceived by him, is not 
an attempt to enumerate the highest classes into which 
things in general can be distributed ; for this would be a 
purely metaphysical speculation, and, as such, open to 
criticism on metaphysical grounds. But it is a classification 
of things in so far only as these things are predicates, — 
that is, of things considered merely in one of their logical 
aspects. To such a classification, metaphysical objections, 
lilce those of Kant, Mill, and Hamilton, are evidently 
irrelevant. For instance : — metaphysically, Place is in- 
cluded under Relation, for it is the relation of a subject 
to a fixed point in space. But, logically, these two Gate- 



120 THE DOCTRrNE OF JUDGMENTS. 

gories are distinct, for it is one thing to assign a Subject 
to a fixed point in space ; a second, to assign its relation to 
another thing in quantity or quahty ; and a third and fourth, 
to assign its quantity and quahty absolutely. Aristotle's 
scheme or general conception of the Categories may be 
censured, as depending on a mixture of two incongruous 
aspects of Thought, the logical and the metaphysical; but 
for all that appears, it is as well executed as such a hybrid 
scheme can be. 

2. The Quantity, Quality, and Relation of Judg- 
ments, ACCORDING TO THE ArISTOTELIC DoCTRINE. 

The question now arises, how many things can be de- 
termined about a Judgment considered merely as such, — 
that is, by considering its mere Form, without reference 
to the Matter of the Concepts which are its Terms. In 
the first place, we may inquire concerning the number 
of objects about which we judge, and thus determine the 
Quantity, or Extension, of the Judgment. Secondly, we 
may ask what sort of a Judgment we form respecting the 
two Terms, — that is, whether we affirm a relation of 
agi'eement or of disagreement between them ; we thus 
ascertain the Quality of the Judgment, or whether it is 
affirmative or negative. Thirdly, we may inquire respect- 
ing the diffiirent modes in which a relation of agreement 
or diffiirence between the two terms may be affirmed, and 
thus determine what is called the Relation of a Judgment. 
In this manner are answered the three questions which 
may be asked concerning any Judgment or Proposition 
whatsoever, — Quanta ? qualis f quce ^ 

A fourth question has generally been asked by logicians, 
as to the degree of certainty with which a Judgment is 
affirmed. This was called the Modality of the Judgment, 
beinff the mode or measure in which we hold it to be true. 



TUEIR QUANTITY, QUALITY, AND RELATION. 121 

Several degrees of it were usually distinguished, according 

to the followins formulas : — 

Judgments are either 

Pure A is B. Assertorical. 

( A may be B. Contingent or Problematic. 

-,,■,, ) A must be B. Necessary. ) 

Jjioaai ^ ^ ^^^^^^ j^ jj Impossible. ; Demonstrative. 

^ A can be B. Possible. 

But the whole doctrme of Modality is now rightfully 
banished from Pure Logic, as it evidently belongs not to 
the Form, but to the Matter, of Thought. Any number 
of Modal Propositions may be framed, all of which would 
have as good a claim to consideration as those just specified. 
Thus, A is rightfully B, A is justly B, A is maliciously 
B, are as good Modals as A is possibly B, or A is certainly 
B. In truth, since the Copula in Logic is only a sign 
of equality, or the present tense of the verb to he, the 
qualifying word must be logically regarded as a portion 
of the Predicate ; thus, A is a possible, or a necessary B. 
Hence it is manifest that the signs of Modality belong 
to the Matter of the Thought, with which here we have 
no concei'n. 

In respect to Quantity, according to the Aristotelic 
logicians, Judgments are either Universal or Particular. 
A Universal Judgment is one in which the Predicate is 
affirmed of the whole Subject taken distributively. Thus, 
All men (i. e. each and every man) are mortal ; No quad- 
ruped (i. e. not any one out of all quadrupeds) is rational ; 
are Universal Judgments. 

A Particular Judgment is one in which the Predicate 
is affirmed only of a part — an indefinite part — of the 
Subject. For example : Some men (i. e. some at least, 
some — I know not how many} are learned; Some trees are 
not deciduous. 

On the other hand, all taken collectively (as, All the 
Greeks — i. e. the Greek nation — conquered the Persians} ^ 



122 THE DOCTRINE OF JUDGMENTS. 

is the sign of a Singular or Individual Judgrrient, in which 
a Predicate is affirmed of one thing, or of a class of things 
taken as one whole. But as here also the Predicate is 
affirmed of the whole Subject, Singular Judgments, for all 
logical purposes, are considered as Universals. 

In like manner, some certain — some, a definite part — 
embracing these very cases which I am thinking of and 
no other — is the sign, not of a Particular, but of a 
Singular Judgment, and is therefore properly ranked with 
Universals. 

" Individual names," says Mr. Mansel, " are distin- 
guished as individua signata, expressed by a proper name, 
as Socrates; iyidividua demonstrativa, by a demonstrative 
pronoun, hie homo ; individua vaga^ by an indefinite pro- 
noun, aliquis homo, quidam homoy But he properly ob- 
jects that this last class, the indefinites, ought to be consid- 
ered as Particulars rather than as Singulars. " If we say 
quidam conscionatur, quidam legit, there is no evidence that 
the same person is spoken of in the two propositions ; while 
Socrates, except by a mere quibble, will always designate 
the same person. There may, indeed, be two persons of 
the same name ; but, in this case, the name fails to accom- 
plish the intended distinction, and we must specify, — Soc- 
rates the son of Sophroniscus." 

The logicians formerly distinguished another class of 
Judgments as Indefinite, meaning those in which the Sub- 
ject, having no sign or predesignation of Quantity affixed 
to it, is not expressly declared to be either Universal, Sin- 
gular, or Particular. Thus, Elephants are sagacious ani- 
mals ; — Learned men are to he found at Oxford. But this 
omission of the predesignation of Quantity is merely an 
accident of expression, and therefore belongs only to Propo- 
sitions, and not to Judgments, which are always thought as 
havmg some one of the three specified kinds of Quantity. 
According to the Postulate of Logic, which requires us to 



THEIR QUANTITY, QUALITY, AND RELATION. 123 

state explicitly all that is implicitly thought, the two exam- 
ples just given are logically stated thus : All elephants are 
sagacious ; — Some learned men are found at Oxford. 

An improved classification or nomenclature of Judgments 
in respect to Quantity is proposed by Sir William Hamilton. 
Since both Universals and Singulars have a determinate or 
known Quantity, — namely, the whole either of a class or 
of a unit, — he would call them Definite Judgments ; while 
Particulars, expressing an indeterminate or unknown part 
of a whole, should be called Indefinite. But as confusion 
might arise from abandoning technical terms which have 
been so long in use, we shall continue to distinguish Judg- 
ments in respect to Quantity as either Universal or Partic- 
ular, Singular being ranked with the former, and the latter 
expressing an indefinite part. 

In respect to Quality, Judgments are distinguished as 
either Affirmative or Negative., according as they affirm a 
union or a disjunction of their two Teiins. In every real 
Negative Judgment, the negative particle, wherever in 
the sentence it may appear, belongs only to the Copula ; 
since the question always is, whether a union of the 
Subject and Predicate is, or is not., affirmed. Hence the 
presence of a negative particle in the proposition is not a 
sure sign that it is a Negative Judgment, for this particle 
may belong in thought to one of the two Terms. Thus, 

" Nil admirari prope res est una, Numici " ; — 
" Not to admire is all the art I know " ; — 
" ^neas potuit — non vincere Turnum " ; — 

are Affirmative Judgments. This, also, is an affirma- 
tion : — 

" Una salus victis — nullam sperare salutem." 

" The only chance of preservation for the vanquished is, not to hope for 
preservation." 

Hence, by an easy artifice, a Negative Judgment may 
be changed, in Form., to an Affirmative one of equivalent 



124 THE DOCTRINE OF JUDGMENTS. 

meaning, by taking off the negation from the Copula, and 
affixing it to the Predicate. Thus, X 18 not Y, is the 
same as, X is not-Y ; for if the universe is divided into 
only two parts, Y and not-Y, the exclusion of X from one 
of these parts is necessarily an inclusion of it in the other. 
And as two negatives cancel each other, an Affirmative 
may be made to take the Form of a Negative Judgment, 
by negativing both the Copula and the Predicate. X is 
Y, may be changed into, X is not not-Y. " The soul is 
indivisible," is equivalent to " The soul is not divisible " ; 
and " All the righteous are happy," is the same as " Not 
any of the righteous are unhappy." We shall soon see 
what use can be made of this artifice in the doctrine of 
Immediate Inference. 

By combining the Quantity and Quality, as there are 
two kinds of each, we have four distinct forms of Judg- 
ments, which are designated by the four vowels A, E, 
I, O. To aid the memory, these distinctions have been 
expressed in this Latin distich : — 

Asserit A, negat E, sed aniversaliter ambae, 
Aaserit I, negat O, sed particulariter ambo. 

These Imes have been thus translated into English dog- 
gerel : — 

A, it affirms of this, these, all, 

Whilst E denies of any ; 
I, it affirms, whilst O denies, 

Of some (or few or many).* 

Examples of these Prepositional Forms, as they are 
called, are given in the following table : — 

Symbols. Examples. Quality. Quantity. 

A. All animals are sentient. Affirmative. ? y-r • i 

E. No plant is sentient. Negative. | ^J^versal. 

I. Some men are honest. Affirmative, f p ^- i 

O. Some trees are not maples. Negative. j 

* It is suggested by Hamilton, with great plausibility, that these four 
letters were selected because A and I are the first two vowels in affimw, E 
and O the two vowels in nego. 



THEIR QUANTITY, QUALITY, AND RELATION. 125 

Observe, however, that though the predesignation all 
is the sign of A, a Universal Affirmative, not all is not 
the sign of E, a Universal Negative, but is always Par- 
ticular, and leaves the Quality ambigiious, as it may be 
either Affiraiative or Neo;ative. Not all denies univer- 
sality, and is a direct assertion that some are not, and an 
implied assertion that some are. Thus, iVb^ all is gold that 
glitters, asserts directly that some glittering things are not 
gold, and, by implication, that some glittering things are 
gold. " Not every one who says unto me, Lord ! Lord I 
shall enter into the kingdom of Heaven " ; — i. e. some 
who say this shall not enter. 

The predesignation some is likewise ambiguous. It may 
mean some at least, — i. e. some, perhaps all; or it may 
mean some at most, — i. e. some, not all. Thus, a chemist 
might say. Some metals are dissolved by adds, meaning 
" Perhaps all metals are Urns soluble, but at any rate, some 
are.'''' On the other hand, he may say. Some metals are 
malleable, meaning, some — excluding all, for he knows that 
some metals are not malleable. In a Negative Judgment, 
if we consider some to mean perhaps all, it is evident that 
" Some X is not Y " may be construed " Perhaps no X is 
Y " ; but if some signifies not all, then some is not excludes, 
or is inconsistent with, nx)ne — n/)t one. The wholly indefi- 
nite meaning, some, perhaps all, is the one generally re- 
ceived in Logic ; the other meaning is called by Sir W. 
Hamilton semi-definite, because, by excluding all, it is so far 
definite. Though this latter meaning has been generally 
neglected by logicians, it leads, as we shall see hereafter, 
to some important additional inferences, and modifies, to a 
considerable extent, the old doctrines concerning Opposition. 

Hitherto we have considered the Quantity of the Judg- 
ment only, and we have now to consider the Quantity of 
the two Terms as affected by the Judgment in Avhich they 
stand. A Term is said to be distributed when it is taken 



126 THE DOCTRINE OF JUDGMENTS. 

distributivelj, or in the whole of its Extension, — that is, 
when it is affected, or should be affected, by the predesig- 
nations all, each, none, &c. ; it is not distributed when it is 
taken only in an indefinite part of its Extension, — as 
usually signified by the predesignations some, not all, &c. 
The received or AristoteKc doctrme upon this matter is, 
that the distribution of the tSubject depends upon the Quan- 
tity/ of the Judgment, thus ; — in Universal Judgments, the 
Subject is distributed, but in Particular Judgments, it is 
not distributed. No unjust action is expedient; — this is a 
Universal Proposition, and its Subject is e"vddently dis- 
tributed, as the meaning is, not any one out of all unjust 
actions is expedient. But in the Particular Proposition, 
Some men are learned, it is obvious that the Subject, men, 
is not distributed. 

On the other hand, the distribution of the Predicate 
depends upon the Quality of the Judgment, thus ; — in 
Negative Judgments, the Predicate is distributed, but in 
Affirmatives, it is not distributed. This rule is evidently 
founded upon the doctrine that all predication is classifica- 
tion ; and consequently, that when we affirm, we thereby 
include the Subject in the class denoted by the Predicate, 
not meaning that the Subject constitutes the whole of that 
class, but only a part of it ; and that, when we deny, we 
thereby exclude the Subject wholly, or from any part of 
the class. Thus, when we say, " Men are animals," we 
mean, " Men are some animals," since it is not true that 
all animals are men. On the other hand, when we say, 
" No man is immortal," we mean to exclude man from 
every part of the class of " immortal beings," so that no 
immortal whatever can be human. And even in the case 
of Particular Negatives, as, " Some Frenchmen are not 
Parisians," we still mean absolute or total exclusion, — 
that not any Parisian whatever is one of the " Some 
Frenchmen " — say, inhabitants of Lyons — whom we were 
speaking of. 



THEIR QUANTITY, QUALITY, AND RELATION. 127 

According; to this doctrine, the four fundamental Judo;- 
ments, if the statements are intended to convey the whole 
Thought which is impUed in them, must be thus ex- 
pressed : — 

A. All X are some Y. All animals are some sentient 
beings. 

E. No X is any Y. No plant is ani/ sentient being. 

I, Some X are some Y. Some men are some honest 
persons. 

O. Some X are not ani/ Y. Some trees are not ani/ ma- 
ples. 

Hence the rule for the distribution of the two Terais 
in a Judgment may be thus briefly expressed : — In A, 
only the Subject is distributed ; in O, only the Predicate ; 
in I, neither ; in E, both. 

Those who maintain this doctrine are perfectly aware, 
of course, that the Predicate is sometimes taken universally 
in Affirmative Judgments, as when we predicate either 
Definition or Property ; but they assert that this results 
from considering the Matter, not the Form, of the Judg- 
ment, and therefore is not entitled to notice in Pure Logic. 
And they further maintain, that the Predicate is never 
quantified particularly in a Negative Judgment. Sir W. 
Hamilton, however, as we shall see, has denied both por- 
tions of the doctrine, and, by substituting for it his own 
theory of " the thoroughgoing quantification of the Predi- 
cate," has revolutionized the whole science of Logic. 

In respect to the Relation of the Predicate to the Subject, 
Judgments are divided into simple or absolute, and con- 
ditional. In the former, which are technically called 
Categorical, the Predicate is conceived as a Mark, and is 
therefore absolutely affirmed or denied of the Subject, 
there being no other ground or reason for the attribution 
or denial than what is contained in the Subject itself. All 



128 THE DOCTRINE OF JUDGMENTS. 

Caterjorioal Judgments are included under these two for- 
mulas, A is B^ A is not B. Conditional Judgments are 
those in which the Predicate is affirmed or denied of the 
Subject, not absolutely, but only under some condition 
or prerequisite. This condition may be conceived as pri- 
marily affecting the Subject, or the Predicate, or both; 
and hence we have three forms of Conditional Judgments, 
distinguished as Hypothetical, Disjunctive, and Dilemmatic 
or Hypothetico-Disjunctive. Thus, in respect to Relation, 
we have four kinds of Judgments, as distinguished in the 
following table. 

Caleyorical. A is B, or, A is not B. 

( Hypothetical. If A is B, A is C. 

/~i j-i- 7 ) Disjunctive. A is either B or C. 

Vonaitional. / r..:' 

\ Dilemmatic, or 

I Hypothetico-Disjunctive. If A is B, then C is either D or E. 

In a Categorical Judgment, Man is mortal., there is 
evidently no ground or reason for the attribution but an 
internal one ; the Mark of mortality is conceived as an 
essential attribute of man under all circumstances or con- 
ditions whatsoever. But in each of the other forms, the 
attribution is conditional. In the Hypothetical Judgment, 
If death is a transition to a happier life., then it is desirable., 
we do not affirm absolutely that death is desirable., but 
affirm it only under a condition affecting the Subject, 
death. In a Disjunctive, as, Every deliberate action is either 
good or evil, the condition evidently affects the Predicate, 
as neither of its two forms is affirmed absolutely, but 
either is affirmed only on condition that the other is de- 
nied. The Dilemmatic, as it has two conditions, the 
one affecting the Subject and the other the Predicate, is 
obviously a combination of the two preceding forms, and 
is therefore properly called the Hypothetico-Disjunctive. 
All Hypothetical Judgments obviously consist of two parts, 
the first of which is called the Condition or Antecedent., 
and the second, the Consequent; and the assertion or 



THEIR QUANTITY, QUALITY, AND RELATION. 129 

Judgment is, that if the Condition exists, the Consequent 
follows. 

A Conditional Judgment, though seemingly complex, is 
really simple, and expresses only a single act of Thought ; 
it contains but one assertion. Thus, in the Hypothetical 
just cited, we do not assert that death is a transition^ or 
that death is desirable ; but only, if it is a transition, then 
it is desirable. Hence the affirmation is evidently single, 
and the particles if and then form the Copula of this 
Judgment, as they connect its two parts together. In a 
Disjunctive, either is and or is form the Copula, which 
reduces an apparently complex Judgment to a simple one. 
Sometimes where and there take the place of if and then 
in a Conditional Judgment ; as, where fire zs, there is heat ; 
where light is, there is shadoiv. 

In Hypotlieticals, the Consequence, or tie which binds 
together the Antecedent and the Consequent, may be 
either mediate or immediate. It is Mediate, only when 
there is nothing in the Terms of either of the two parts 
which binds them together ; as when we say, 

If A is B, Q is D. 

If the air is still and cloudless, the deiv will fall. 
If Grod is just, sinners will he punished. 

In such cases, the Consequence may be valid, but it is 
not Immediate ; for, as there are four distinct Terms, the 
two Parts have no common Term, and are therefore con- 
nected only by some unknown cause, or by what is in the 
mind, but is not expressed. The unexpressed medium, 
which binds the two Parts together in the last case, is our 
knowledge that Grod governs the world, and that justice 
consists in rewarding the good and punishing sinners; there- 
fore, if God is just, sinners will be punished. 

The Consequence is Immediate, when there are only 
three Terms in the two Parts, so that, since one of these 

6* I 



130 THE DOCTRINE OF JUDGMENTS. 

Terms is necessarily repeated, it forms an immediate con- 
nection of the Parts with each other. In order that 
there may be this repetition of one of the Terms, either 
the two Parts must have the same Subject, or the same 
Predicate, or the Predicate of the first must be the 
Subject of the second, or the Subject of the first must 
be the Predicate of the second. In other words, the 
Hypothetical must appear under one of the four following 
formulas. 

If A is B, A is C. If men do wrong ^ they deserve pun- 
ishment. 

If A is B, C is B. if metals are fusible, gold is fusible. 

If A is B, B is C. Jf patience be a virtue, virtue may 

be painful. 

If A is B, C is A. If happiness is mere freedom from 

pain, insensibility is happiness. 

In each of these cases, the Consequence is Immediate, 
becaiise it results from a general rule, which is presupposed 
in the Proposition that is before us, and may be evolved 
from it without any further appeal to experience. Because 
"all C is A," we can immediately infer that, "if A is B, 
C is B " ; or conversely, because the latter Proposition 
is miiversally true, the former can be deduced fi'om it by 
necessary implication. If the earth is immovable, and is 
lighted in all parts by the sun, the sun revolves round it ; — 
this is true so far as concerns the dependence of the one 
Proposition upon the other, though either Proposition, 
taken separately, is false. Hence, we do not deny a 
Hypothetical Judgment by denying either or both of its 
parts, but only by denying the Consequence of one ft-om 
the other. This is usually done, in Latin, by placing the 
negation at the beoinnino-. 

Non si miscrum fortuna Sinonem 
Finxit, vaiiura ctiara incndaccmque improba finget. 



THEIR QUANTITY, QUALITY, AND RELATION. 131 

In English, we may deny a Hypothetical by substituting 
although, or some equivalent, for if in the Reason, and 
then negativing the Consequent. 

If yon eat of the forbidden fruit, you shall die. 
Although you eat, ^., you shall not die. 

Or the Proposition may be thus denied. 

It is not true that if you eat, ^c. 

Disjunctives are denied in the same manner. 

Conditional Judgments can be reduced to Categoricals, 
though, for logical purposes, it is more convenient to retain 
them in the Conditional form. The Condition is equiva- 
lent to a limitation, and therefore can always be expressed 
by a limiting adjective (see page 143). In the formula. 
If A is B, then A is C, it is not asserted that all A is C, 
but only those A which are B. Let d represent such A ; 
then the equivalent Categorical formula is, dA are C. 
To take a concrete instance : — If the iron is magnetic, it 
has the attribute of polarity ; this is equivalent to the 
Categorical Judgment, magnetic iron is polar. Conversely, 
if any Categorical Judgment has its Subject limited by a 
qualifying word, the limitation can be resolved into a 
condition, and the Judgment thus becomes Conditional. 
Thus, Virtuous men are happy, is equivalent to If men are 
virtuous, they are happy. 

Disjunctives are reduced in a similar manner to as many 
Categoricals as there are disjunct members of the Predi- 
cate. Thus, — 

( All those A which are not B are C, 
A is either B or C = < and 

( All those A which are not C are B ; 

and if d represents the former and / the latter, we have 
dA are C, and fA are B. Even then, the Thought is not 
complete until we add, dA -j- fA = all A. It amounts 
to the same thing to say, that a Disjunctive may be first 



132 THE DOCTRINE OF JUDGMENTS. 

resolved Into as many Hypotheticals as it has disjunct 
members ; and each of these may, then be reduced, as 
before, to a Categorical. Thus, If A is not B, it is C ; 
and. If A is not (7, it is B. Evidently, then, Disjunctives 
are only complex Hypotheticals. 

3. The Hamiltonian Doctrine of Judgments. 

According to the Aristotelic doctrine, as we have seen, 
in all Affirmative Judgments, the Predicate is Particular, 
while in all Negative Judgments it is Universal. Thus 
we have but four fundamental Judgments or Propositional 
Forms, which have been designated by the four vowels 
A, E, I, and O. According to Sir William Hamilton's 
doctrine of " the thorough-going quantification of the 
Predicate," in both Affirmative and Negative Judgments, 
the Predicate may be distributed or undistributed, — that 
is, may be either Universal or Particular. This doctrine 
gives us eight Propositional Forms, which are thus indi- 
cated : — A signifies that the Term to which it corresponds, 
whether Subject or Predicate, is universal, whilst /signifies 
that it is particular ; f* standing in the place of the 
Copula, signifies that the Judgment is affirmative, whilst 
n* signifies that it is negative. Thus we have the follow- 
ing table of Hamilton's eight fundamental Judgments, 
those of them wliich are recognized under the Aristotelic 
doctrine being also indicated, as before, by the four vowels. 

Affi,rmatives. 

Afa. All X are all Y. e. g. All copperas is all sulphate of Iron. (1.) 
(A.) Afi. All X are some Y. " All whales are some mammals. (2.) 

Ifa. Some X are all Y. " Some men are all logicians. (3.) 

(I.) Ifi. Some X are some Y. " Some quadrupeds are some amphib- 
ious. (4.) 

* These two letters are selected because they are the two first consonants 
of affirmo and nego. 



THE HAMILTONIAN ANALYSIS. 133 

Negatives. 

(E.) Ana. Not any X is any Y. e. g. Not any fish is any warm- 
blooded. (5.) 
Ani. Not any X is some Y. " Not any Englishman is some 

Briton (Scotch). (6.) 

(O.) Ina. Some X are not any Y. " Some Frenchmen are not any 

Parisians. (7.) 

Ini. Some X are not some Y. " Some trees (oaks) are not some 

trees (maples). (8.) 

The question is, whether these four Forms, \\z. Afa, Ifa, 
Ani, and Ini, which have been added to the list by Sir 
W. Hamilton, are legitunate and natural Forms of Thought, 
— whether we do not have frequent occasion to think them 
as Judgments, though we seldom or never express them as 
Propositions. It is admitted that the predesignations of 
quantity, some, a??, any, here italicized as belonging to the 
Predicate, are usually elided in expression. This is the case 
even with the old Forms, A, E, I, and O ; for language 
aims always at brevity, and therefore usually omits all that 
is so obvious as to be easily understood, since its expression 
would only cumber and lengthen the sentence unnecessari- 
ly. Thus, we usually say, Men are animals ; but nearly all 
logicians acknowledge that the Thought, of which this is an 
abbreviated expression, is. All men are some animals. But 
the peculiar function of Logic is to analyze, not language, 
but Thought ; it deals, not with Propositions, but with Judg- 
ments. Hence its necessary postulate, that we must be 
allowed to express logically all that is contained in what 
we think. The question is, whether we are not often 
obliged to think Judgments under the Forms, All are all. 
Some are all. Not any is some, and Some are not some. 

Now the evidence in favor of the first two of these 
Forms, the affirmatives Afa and Ifa, is so strong, that the 
only wonder is, how they could have been almost univer- 
sally rejected by logicians for over two thousand years, 
down to the time of Sir W. Hamilton. In the first place, 



1S4 THE DOCTRINE OF JUDGMENTS. 

any process of inductive reasoning can be properly reduced 
to logical Form only in this manner : — 

X, y, Z, &c. are B. 

But X, Y, Z, &c. are (or represent) all A. 

Therefore, all A are B. 

Here the second premise is materially false ; but with 
this fault, as logicians, we have nothing to do. Logic does 
not guarantee the truth of the premises, but only the validi- 
ty of the inference from the premises to the conclusion. 
And that this inference is valid in the preceding formula 
may be seen by taking an instance in which neither of the 
premises is faulty. If I am playing chess, and my king is 
in fatal check, I must reason thus : — 

I can neither move my king, nor interpose a man, nor 
capture the attacking piece. 

But these three are all the modes of obviating check. 

Then I am checkmated. 

Here the Predicate of the second premise is quantified 
universally; and men reason in this manner every day, 
when they are reduced to a choice among a few only possi- 
ble modes of action, and each of these modes is fatal. The 
following example shows how we reason inductively : — 

Copper, tin, lead, iron, &c. are fusible. 

But copper, tin, lead, &c. are (or represent) all metals. 

Then all metals are ftisible. 

As already hinted, every adequate Definition — that is, 
every one in wliich the Definiendum and the Definition are 
convertible terms — has its Predicate universally quantified 
in Thought. To take the instance already given. All cop- 
peras is sulphate of iron, or, conversely. All sulphate of iron 
is all copperas. So, also, every exhaustive Division must 
be thought as a Judgment with a universal Predicate. 
Thus, the geometer, having demonstrated a certain prop- 
osition successively of equilateral, isosceles, and scalene 
triangles, adds in Thought, But these are all triangles; 
therefore, the theorem holds good of all triangles. 



THE HAMILTONIAN ANALYSIS. 135 

*' In fact," says Hamilton, " ordinary language quantifies 
the Predicate so often as this determination becomes of the 
smallest import. This it does directly, by adding all^ some, 
or their equivalent predesignations, to the Predicate ; or it 
accomplishes the same end indirectly, in an exceptive or 
limitative form. 

"*) Directly, — as, Peter, John, James, etc. are all the 
Apostles ; — Mercury, Venus, etc. are all the planets. 

" •*) But tliis is more fi-equently accomplished indirectly, 
by the equipollent forms of Limitation or Inclusion, and 
Exception.* 

" For example, by the limitative designations, ahne or 
only, we say, God alone is good, which is equivalent to 
saying, Crod is all good, that is, €rod is all that is good; 
Virtue is the only nobility, that is. Virtue is all noble, that 
is, all that is noble. The symbols of the CathoHc and 
Protestant divisions of Christianity may afford us a logical 
illustration of the point. The Catholics say, Faith, Hope, 
and CJiarity alone justify ; that is, the three heavenly virtues 
together are all-justifying, that is, all that justifies ; omne 
justificans, justum faciens. The Protestants say, Faith 
alone justifies ; tliat is, Faith, which they hold to comprise 
the other two virtues, is all-justifying, that is, all that 
justifies; omne justificans. In either case, if we translate 
the watchwords into logical simphcity, the predicate ap- 
pears predesignated. 

" Of animals man alone is rational ; that Is, Man is all 
rational animal. What is rational is alone or only risible; 
that is. All rational is all risible, etc. 

" I now pass on to the Exceptive Form. To take the 
motto overhead, — ' On earth there is nothing great but 
man.' What does this mean ? It means, Man — is — all 

* The English Exclusive particles are, one, only, alone, exclusively, pre' 
cisdy, just, sole, solely, nothing, but, &c. These particles annexed to the Sub- 
ject prcdcsignate the Predicate universally, or to its whole extent. 



136 THE DOCTRINE OF JUDGMENTS. 

earthly great. QHomo — est — omne magnum terrestre.') 
And the second clause — ' In man there is nothing great 
but mind ' — in Hke manner gives, as its logical equipollent, 
Mind — is — all humanly great^ that \s, all that is great in 
man. (^Mens est omne magnum humanum.y^ 

The case may not seem so clear in respect to the two 
negative Forms, Ani and Ini, in which the Predicate is 
Particular ; for the expression of them in language is so 
awkward and unnatural as to have provoked the remark, 
that thej seem to be got up as if for the purpose of show- 
ing what one could do. It would certainly be accounted a 
forced and uncouth assertion, to say that not any iron is 
some metal^ — i. e. is not lead ; or that some men (Enghsh- 
men) are not some men (Frenchmen). Dr. Thomson ad- 
mits that they are conceivable^ but denies that they are 
actual^ cases of negative predication. He argues that 
" such a Judgment is never actually made, because it has 
the semblance only, and not the power, of a denial. True 
though it is, it does not prevent our making another Judg- 
ment of the affirmative kind from the same Terms." It 
would be more correct to say that we can make " another 
Proposition," instead of " another Judgment," from the 
same Terms ; for the " some metal " in the Predicate of the 
negative Judgment is not thought as the same "some metal" 
in the Predicate of the affirmative. The two assertions 
are incompatible in Thought, though they happen to be 
identical in expression. Thus, — 

Iron is not some metal, — i. e. is not lead. 

Iron is some metal, — i. e. is iron. 

Englishmen are not some men, — not Frenchraen. 

EngHshmen are some men, — EnglishvaQU. 

In fact, the law of Division, that the Dividing Members 
must exclude each other, compels us to think some are not 
some^ — these are not those^ — these are different from those. 
As already shown, negation is only the affirmation of dif- 



THE HAMILTONIAN ANALYSIS. 137 

ference or exclusion ; ' A is not B,' is equivalent to ' A is 
not-B.' Now we never have occasion to affirm difference 
or exclusion except for the puqjose of distinguishing co- 
ordinate Species from each other ; for if the two classes were 
not recognized as belonging to the same Genus, — that is, 
as similar in some respects, — it would not be necessary to 
tliink or to say that they differ in certain other respects. 
We never say, Fishes are not stars, since the two things are 
so unlike that there is no danger of confounding them. 
But we think and say, Oaks are not maples. Spaniels are 
not terriers, as the classes are here thought as belonging to 
the same proximate Genera, trees and dogs. In Thought, 
therefore, these two Judgments are explicated thus : Some 
trees are not some trees ; Some dogs are not some dogs. 

Even the Aristotelic doctrine admits that Unskilful are 
some physicians is a legitimate Judgment, for it is the sim- 
ple converse of Some physicians are unskilful. But it 
amounts to precisely the same thing whether we say, Un- 
skilful are, &c., or Not (any) skilful are some physicians. 
Considered as Propositions, one of these may be con- 
demned as faulty in expression ; but as Judgments, one 
cannot be admitted and the other rejected, for they are one 
and the same Judgment. 

Agam, whenever we predicate a Genus of a Species, the 
Predicate is obviously quantified as Particular ; and some, 
which is the predesignation of particularity, must then be 
thought in its semi-definite sense, as some, excluding all. 
In this sense, we cannot think that some are, unless we also 
think that some are not. Then, every such Judgment 
carries with it by necessary inference, or as a part of itself, 
another Judmnent, neirative in Form and with a Particular 
Predicate. Thus the Judgment, Men are some animals 
(rational bipeds), is incomplete and even impossible in 
Thought, unless we also think, Men are not some (other) ani- 
7iials (brutes). Either of these two assertions thus carrying 



138 THE DOCTRINE OF JUDGMENTS. 

the other along with it by necessary implication, it is more 
natural to adopt in words the affirmative form, as the more 
frequent and familiar one, even when the negative meaning 
is more prominent in Thought. As Hamilton remarks, 
" men naturally preferred to attribute positively a part of 
one notion to another, than to deny a part." 

It has already been argued, (page 110,) that although 
the Predicate in any Judgment may be actually thought 
only connotatively^ or as a Mark, it is stiU potentially a 
Concept, and as such, it denotes a class, or has Extension. 
To predicate, therefore, is virtually to classify, or to as- 
sign a Subject to its proper place in a class, thereby attrib- 
uting to it all the Marks of that class. Now it is argued 
by Mr. Baynes, with great force, " that when we bring an 
object under a notion, that is, when we predicate of it 
that it belongs to such a class, we must know that it occu- 
pies axcertain place in that class. For if we were uncer- 
tain what place the individual object occupied in the class, 
or whether it occupied any place at all, we should not 
know the class, and could not therefore bring any object 
under it ; — e. g. if I do not know whether rose comes 
under the Concept fiower^ — whether it is equal to some 
part, or the whole, or superior to it, — I cannot, of course, 
predicate flower of rose, since I do not know what the 
Concept means, what it contains, and what it does not. 
If, therefore, we understand the object at all, we must fix, 
in Thought, the sphere which it occupies imder the class to 
which, in predication, we have assigned it. In other words, 
if we comprehend wliat we utter, every notion holding the 
jjlace of predicate in a proposition must have a determinate 
quantity in thought.^'' * We cannot, for instance, predicate 
bird successfully of pigeons, of winged and feathered bipeds, 
and of animals, unless we know at least so much of the 
characteristics of the class bird as to be able to tliink that 

* Baynes's Ntw Atialytic of Loyical Forms, pp. 9, 10. 



THE HAMILTONIAN ANALYSIS. 139 

" all pigeons are some birds," " all winged and feathered 
bipeds are all birds," and "some animals are all birds." 
In like manner, we cannot exclude a Subject from a given 
Concept or class, — as when we say, Whales are not fish, 
unless we either think fish as cold-blooded, vertebrated ani- 
mals, living in the water and breathing by gills, in which 
case we think " whales are not any fish " ; or accept the 
vulgar notion of fi^h as finned animals living in the water, 
and then think " whales are not some fish," — viz. not cold- 
blooded fish. This leads us to remark, that, in fact, any limi- 
tation of the predicated class by a limiting adjective is equiv- 
•alent to quantifying that Predicate particularly ; — e. g. 
Pines are not deciduous trees = Pines are not some trees. 

These reasons, and others which will be mentioned when 
we come to treat of Conversion, seem conclusive in favor 
of Sir W. Hamilton's doctrine, that, potentially at least, 
the Predicate is always quantified either universally or par- 
ticularly, both in affirmative and negative Judgments. 

But if each of the two Terms of a Judgment has its own 
quantity assigned to it in Thought, then, for still stronger 
reasons than those which have already (pp. 64, 110) been 
assigned, the distinction between Subject and Predicate 
ceases to be of any moment. In fact, every Judgment 
comes from an act of comparing two quantified Terms with 
each other ; and as the result of such comparison, we have 
an equation, or non-equation, established between these 
Terms, and it is completely indifferent which of them is 
placed first. Thus, having compared two Concepts, A and 
B, I find either that they agree, or do not agree, with each 
other. This agreement or difference may be expressed 
equally well in either of the following formulas : — 

A is B. A is not B. 

B is A. B is not A. 

A and B are equal. A and B are not equal. 

Convertible or equal are A and B. Unconvertible are A and B. 



140 THE DOCTRINE OF JUDGMENTS. 

In these last two formulas, the two compared notions do 
not stand to each other as Subject and Predicate, but are, 
in the same proposition, either both Subjects or both Predi- 
cates. 

In common language, if the two Terms are both quanti- 
fied universally in Thought, it is admitted to be of no 
consequence which is placed first; usually, that which is 
prior or pre-emment in Thought appears as the Subject. 
Thus, we say either, Electricity is not the nervous fluid, or, 
The nervous fluid is not electricity ; Common salt is chloride 
of sodium, or. Chloride of sodium is common salt. 

But if the two Terms differ in Quantity, the convenience 
of language requires, in most cases (not in all *), that tlie 
one which has the wider Extension should appear as the 
Predicate, and that its Quantity, though present in Thought, 
should be silently passed over in expression. It is more con- 
venient that the Term which has the less Extension, as it is 
more definite or hraited in meaning, and therefore can be 
more easily grasped in Thought, should be placed first ; and 
then, the Quantity of the Predicate, as it is known to be 
greater than that of the Subject, (and it matters not how 
much greater it is,) may be omitted in expression for the 
sake of brevity. Metals are fusible suhstances is a shorter 
and more natural expression than Some fusible substances 
are metals, though the two propositions convey precisely 

* Such propositions as these, for instance, are common : — 

It is disgraceful to be a slave to passion. 

Turpe est obsequi lihidini. 

Happy is he who is able to know the causes of things. 

Felix qui potuit rerum cognoscere causas. 

It is rain which has fallen. 

It is foolish to listen to flatterers. 

If the Term of the wider Extension must be the Predicate, we should 
say, — To be a slave to passion is disgraceful ; He who can discover the causes 
of things is happy ; That which has fallen is rain ; To listen to fUilterers is 
folly. 



EXPLICATION OF PROPOSITIONS INTO JUDGMENTS. 141 

the same meaning. Hence the old logicians, having more 
regard to Language than to Thought, maintained that the 
former order was the only legitimate one ; they analyzed 
this order only, and based upon it their whole system. 
" Natural, or regular, or direct predication they held to be 
that in which the genus is predicated of the species, the 
species of the individual, the attribute of its subject, and, 
in general, the extensive whole of its part ; and in which, 
therefore, the Subject notion was always of less extent than 
the Predicate notion. Unnatural, indirect, or irregular 
predication was the reverse of this, — that, to wit, in which 
the species was predicated of the genus, the subject of its 
attribute, and, in general, the extensive part of its whole."* 
But when it is acknowledged that Logic has to do pri- 
marily with Thought, and only secondarily with Lan- 
guage ; that each of the two Terms has its own Quantity 
assigned to it in Thought ; and that the purport of the 
Judgment is merely to affirm the agreement or non-agree- 
ment of these two quantified Terms, — it becomes evi- 
dent that every proposition is logically reduced to an 
equation, or non-equation, of two Terms, the relative posi- 
tion of which is of no importance whatever. All metals 
are some fusible things^ and Some fusible things are all met- 
als, are two statements of precisely the same import. And 
in like manner with negatives ; — Some Frenchmen are 
not any Parisians, is the same Judgment as, Not any Pa- 
risians are some Frenchmen. 

4. The Explication of Propositions into Judgments. 

Strictly speaking, as we have seen. Pure Logic deals 
only with Judgments, and refers to the science of Lan- 
guage for the doctrine of Propositions, or the proper ex- 
pression of Judgments in words. But the claims of Logic 

* Baynes's Aiiali/tic, p. 12. 



142 THE DOCTRINE OF JUDGMENTS. 

to be regarded as a universal science, and its doctrine that 
all Thought can be reduced to distinct Judgments, so that 
the logical theory of Judgments is appHcable to every 
mental product into which Thought enters, cannot be de- 
fended, or even properly understood, until it is clearly 
shown how all Propositions, even the most complex in 
character, may be reduced to simple Judgments. We 
shall therefore consider the explication of Propositions 
here, though the subject properly belongs to Applied 
Logic. 

Every pure Judgment corresponds to one of these two 
forms, — A is B, or A is not B ; and if thus expressed in 
words, it is called a Simple Proposition. In this case, 
neither Subject nor Predicate necessarily consists of a 
single word ; either or both may be described in many 
words, provided that the union of these words expresses 
but one Judgment or a single act of Thought. Thus, Well 
organized and skilfully administered governments are produc- 
tive of happiness to their subjects^ is a Simple Proposition, as 
well as John is sick. On the other hand, several acts of 
Thought combined in one statement constitute a Compound 
Proposition, the plurality of which may reside either in the 
Subject, or in the Predicate, or in both. Thus, James and 
William are young and healthy^ is a Compound Proposition, 
which may be resolved into these four Simple ones : — 
James is young; James is healthy; William is young; 
William is healthy. A distinct Judgment is evidently ne- 
cessary for each of these affirmations, whether they are 
expressed separately, or united into one Compound Propo- 
sition. Such a Proposition obviously may be partly true 
and partly false, according as all, or only some, of the Predi- 
cates are truly affirmed of all, or only some, of the Sub- 
jects. 

But as a Simple Proposition contains only one Subject 
and one Predicate, it would seem that it must be either 



EXPLICATION OF PROPOSITIONS INTO JUDGMENTS. 14? 

wholly true or wholly false. And so it would be, but tha^ 
there are many Propositions, seemingly Compound, bu' 
really Simple, whose Subject or Predicate is a Complex 
term, containing by implication other Judgments, that ma^* 
be called incidental. In these, the incidental Judgment 
may be false, while the main Proposition may be true. In 
those which are properly called Complex Propositions, the 
incidental or implied Judgment may appear, either as a part 
of the Subject or of the Predicate, with which it is joined 
by a relative pronoun, whose office it is to combine severaJ 
Propositions into one, or only as a limiting or defining ad- 
jective, or participle, or adjective clause. Thus, it is the 
same thing to say, Crod, who is invisible, created the world, 
which is visible; or. The invisible God created the visibU 
loorld. It is justly remarked by the Port Royal Logi- 
cians, that these incidental Judgments are to be regarded 
not so much as Propositions which we now make, but a? 
Judgments /or merZ^ made, the Predicate of which is now 
regarded as a simple Mark or attribute of one of the 
Terms in our present main Proposition. Hence it is stilX 
ti'ue, that the Complex Proposition is Simple, because it 
expresses but one Judgment made at the moment. 

The incidental Judgment expressed in an additional 
word or clause may be either explicative or limitative. It is 
Explicative, when it is of the nature of a complete or partial 
definition, and therefore belongs to the Term to which it is 
annexed in the whole of its Extension. Thus, Man, who 
is born of woman, is of few days and full of trouble; — 
here, the adjunct clause, horn of woman, is to be understood 
as a definition applicable to all men. But in such a Propo- 
sition as this, Mef)i who are avaricious are unhappy, the 
relative clause restricts or limits the predication of unhap- 
piness to some men, — to those only who are avaricious. 
It is only these Complex Limitative Propositions which are 
equivalent to Hypotheticals : — thus, All iron which is mag- 



144 THE DOCTRINE OF JUDGMENTS. 

netic is polar^ lias the same meaning as, If iron is mag- 
netic, it is polar. It depends upon tlie Matter of the 
Thought, and can usually be determmed by the context or 
the nature of the subject, whether the adjunct word or 
clause is to be considered as Exphcative or Limitative. 

With regard to Explicatives, it should be observed, that 
the falsehood of the incidental does not affect the truth of 
the principal Proposition. Thus, in the Proposition, Har- 
modius and Aristogeiton Jellied Hipparchus, who was a 
tyrant, or, hilled the tyrant Sipparchus, the main assertion 
would still be true, even though Hipparchus was not a 
tyrant. If, however, there is an implied Inference or ar- 
gument, that the principal Proposition is true because the 
incidental one is a correct definition, then the falsity of 
the latter becomes a reason for doubting, not for denying, 
the truth of the former. Thus, the Proposition, TJie soul, 
which is an extended substarice, must occupy space, becomes 
doubtful when the incidental affirmation, that it is extended, 
is dis})roved ; but it may still be true, for other reasons, 
that the soul must have some position in space. 

In respect to Limitative s, no question can arise concern- 
ing the truth or falsity of the incidental Proposition ; for 
its Predicate is not affirmed of the Subject to which the 
relative refers, nor is the existence of any such Subject 
affirmed. If I say. Judges who never do anything by 
request or favor are worthy of praise, the only assertion is a 
Hypothetical one. I do not affirm, that Judges never do 
anything by request or favor, or that there are any such 
Judges ; but only, that if there are any such, then they de- 
serve praise. The most orthodox believer in the atoning 
virtue of the death of Christ may still admit, that a man who 
has never sinned, and is not sinful by nature, stands in no 
need of an atonement. So far, indeed, as such a statement 
contains any implication that such a human being ever 
lived, it is false ; but if construed strictly, it implies noth- 
in<r of the kmd. 



EXPLICATION OF PROPOSITIONS INTO JUDGMENTS. 145 

Compound Propositions are divided into those wliich 
obviously contain a plurality of Judgments, and therefore 
do not need analysis and exposition ; and those in w^hicli 
the plurality is concealed, so that it is apt to escape notice. 
The latter are called Exponibles, because they need to be 
analyzed and explained. These are cUvided into Exclu- 
sives, Exceptives, and Restrictives. 

Exclusive Propositions limit the Predicate to this one 
Subject, thereby excluding it from every other Subject. 
Hence, every Exclusive contains two Propositions, one of 
which affirms the Predicate of A, and the other denies it 
of all not-A. Thus, 

Only A is B = \ ^-, ' . . _ 

'^ \ No not-A IS B. 

i God is to be worshipped. 
God alone is to be worshipped = | iVb other being is to he 

\ worshipped. 

Hamilton, as we have seen, reduces these Compounds 
to Simple Propositions, by showing that the Exclusive 
particle annexed to the Subject quantifies the Predicate 
universally ; thus : — 

Only A is B = A is all B ; 
whence we infer immediately, by Infinitation, that 
M not-A is B. 

Sometimes the Exclusive particles only, one, sole, &c., 
are annexed adjectively to the Predicate, and then have 
the same meaning as all. Thus, God is the sole object to 
be worshipped ; — i. e. God is all that should be worshipped. 

Annexed adverbially to the Copula and Predicate taken 
together, the Exclusive particle limits the Subject to tliis 
one Predicate, thereby excluding it from every other 
Predicate. 

Peter only plays ; i. e. he plays, and he does 7iotldng else. 

James is only a lawyer ; i. e. he is a laivyer, and nothing 

else. 

7 J 



All but one have disappeared : 



146 THE DOCTRINE OF JUDGMENTS. 

But, James is the only lawyer = he is all the lawyer that 
you can find. 

Exceptive Propositions state the Subject universally, yet 
with a specified exception, to which it is implied that the 
Predicate is not attributed. These also are equivalent to 
two Judgments, and these two, as in the case of Exclusives 
also, differ in Quality. 

' (Nearly) all have disap- 
peared ; 
but one has not disap- 
peared. 

In respect to Quantity, Exceptives are to be considered 
as Universals. For although a part is excluded from the 
whole of the Subject, so that the Predicate is referred 
only to the remainder, yet this remainder constitutes a 
whole in itself, of which the Predicate is affirmed or 
denied. 

It is obvious that an Exclusive and an Exceptive are 
only two modes of expressing the same thing, as it is easy 
to change them reciprocally from the one to the other ; 
but the direct affirmation in one becomes the implied 
assertion in the other. A fool thinks that no method ex- 
cept his own is right; in other words, that his own is the 
only right method. 

Restrictive Propositions are of two kinds, both of which 
are Limitative in meanino-. The first sort restricts the 
assertion by a special clause, which determines more nar- 
rowly the signification of the Subject or the Predicate. 
JEtliics, considered merely as a doctrine of the expedient^ is 
no longer a science of morality : — this is equivalent to 
the two Judgments, Ethics is a science of morality, l^ut 
a mere doctrine of expediency is not such a science. Here 
the Subject is the restricted Term ; but in the following 
example, it is the Predicate. A good magistrate is merci- 
ful to offenders, as far as the demands of justice will permit. 



EXPLICATION OF PROPOSITIONS INTO JUDGMENTS. 147 

The second sort of Restriction is called Reduplicative, as 
it consists in a repetition of the restricted Term. A judge, 
as judge, ought never to receive presents ; — that is, he may 
receive them, like other men, on ordinary occasions, but 
never in connection with the performance of his official 
duties. Here, also, the two Judgments into which the 
Proposition is explicated differ in Quality. 



148 THE DOCTRINE OF IMMEDIATE INFERENCE. 



CHAPTER VI. 

THE DOCTRINE OF IMMEDIATE INFERENCE. 

1. -ffiquipollence or Infinitation. — 2. Conversion. — 3. Opposition and 
Integration. 

INFERENCE or Reasoning is that act of Pure Thought 
whereby one Judgment is derived from another, or 
from two others. The Judgment from which another is 
deduced is called the, Premise ; and that which is derived is 
called the Conclusion. If the Conclusion is drawn directly 
fi'om one Premise only, without the aid either of an 
Intuition or another Judgment, it is said to be an Immedi- 
ate Inference. Thus, from the Premise that No quadruped 
is rational^ I know at once, or by Immediate Inference, — 
that is, by an act of Pure Thought, — that Every quadru- 
ped is irrational, and that '^o rational thing is a quadruped. 
If the Conclusion can be drawn only through the interven- 
tion of a third Judgment^ — in other words, if two Prem- 
ises are necessary, — the result is a Mediate Inference, 
or Syllogism. , 

But in either case/ the act of Reasoning or Inference, 
whether Mediate or , Immediate, is simple, being one indi- 
visible act of mind. The Premises are considered as 
given, and their truth is taken for granted ; the Inference 
is the act of deduction, or drawing out the Conclusion from 
the Premises, and this act is necessarily simple. If it is 
perfonned in accordance with the Laws of Pure Thought, 
it is apodeictic or absolutely certain, as any opposite Con- 
clusion would be Contradictory and absm-d. In respect to 



THE DOCTRINE OF IMMEDIATE INFERENCE. 149 

their Matter^ both the Premises and the Conclusion may be 
false ; and yet the Form of Inference, or the transition 
from one to the other, may be intuitively true. Thus, the 
Mediate Inference, 

Everything material is mortal; 

The Soul is material; 

Therefore the Soul is mortal; — 
is false in each of its three Judgments. Yet its Conclusion 
is as coiTectly drawn, and the Syllogism is therefore just as 
valid, as in the following instance, where each of the tlu:ee 
Judgments is true. 

Everything material is divisible; 

Gold is material ; 

Therefore Gold is divisible. 
Hence, the material truth of the Conclusion depends upon 
the material truth of the Premises ; its formal validity is 
the correctness of the process whereby it was deduced from 
the Premises. Pure Logic has to do only with the latter. 
Every correct step of Reasoning, considered simply as such, 
or in reference to its Form, is as indisputable as one of 
those Primary Axioms of Pure Thought on which it is 
based, or of which it is an apphcation. The uncertainty or 
disputable character of much of what is improperly called 
Reasoning hes altogether in the Premises, and is referable 
to imperfect observation, to an improper use of words where 
language has become a substitute for Thought, or to over- 
hasty generalization. But the mere process of Reasoning, 
irrespective of the data about which we reason, is the same 
in the moral and physical, as in the purely mathematical, 
sciences ; it is equally demonstrative in all, for it is condi- 
tioned by the absolute laws of Pure Thought. The long- 
. est chain of argument is but a series or repetition of In- 
ferences, whether Mediate or Immediate, in which the 
formal vahdity of each step, taken by itself, is intuitively 
perceived. 



150 THE DOCTRINE OP IMMEDIATE INFERENCE. 

Logic, as Hamilton remarks, " is exclusively conversant 
about Thought strictly so denominated ; and Thought 
proper, we have seen, is the cognition of one object of 
thought by another, in or under which it is mentally in- 
cluded ; — in other words. Thought is the knowledge of 
a thing through a Concept or General Notion, or of one 
Notion through another. In Thought, all that we think 
about is considered either as something containing, or as 
something contained; — in other words, every process of 
Thought is only a cognition of the necessary relations of 
our Concepts. This being the case, it need not move our 
wonder that Logic, within its proper sphere, is of such 
irrefragable certainty, that, in the midst of all the revolu- 
tions of philosophical doctrines, it has stood, not only 
unshattered, but unshaken. In this respect. Logic and 
Mathematics stand alone among the sciences, and their 
pecuhar certainty flows from the same source. Both are 
conversant about the relations of certain a 'priori foims of 
intelligence ; — Mathematics about the necessary forms of 
Imagination ; Logic about the necessary forms of Under- 
standing ; — Mathematics about the relations of our repre- 
sentations of objects, as out of each other in space and time ; 
Logic about the relations of our Concepts of objects, as in 
or under each other, that is, as in different relations respec- 
tively containing and contained. Both are thus demonstra- 
tive, or absolutely certain, sciences, only as each develops 
what is given, — what is given as necessary, in the mind 
itself. The laws of Logic are grounded on the mere 
possibility of a knowledge through the Concepts of the 
Understanding, and, through these, we know only by com- 
prehending the many under the one. Concerning the 
nature of the objects delivered by the Subsidiary Faculties 
to the Elaborative, Logic pronounces notliing, but restricts 
its consideration to the laws according to which their 
agreement or disagreement is affirmed." 



THE DOCTRINE OF IMMEDIATE INFERENCE. 151 

"It is of itself manifest that every science must obey 
the laws of Logic. If it does not, such pretended science 
is not founded on reflection, and is only an irrational 
absurdity. All Inference, evolution, concatenation, is con- 
ducted on logical principles, — principles which are ever 
vahd, ever imperative, ever the same. But an extension of 
any science through Logic is absolutely impossible ; for by 
conforming to logical canons, we acquire no knowledge, 
receive notliing new, but are only enabled to render 
what is already obtained more intelligible, by analysis and 
arrangement. Logic is only the negative condition of 
truth. To attempt by a mere logical knowledge to amplify 
a science, is an absurdity as great as if we should attempt, 
by a knowledge of the grammatical laws of a language, to 
discover what is written in this language, without a perusal 
of the several writino;s themselves. But thouo;h Logic 
cannot extend, cannot amplify, a science by the discovery 
of new facts, it is not to be supposed that it does not con- 
tribute to the progress of science. The progress of the 
sciences consists not merely in the accumulation of new 
matter, but likewise in the detection of the relations sub- 
sisting among the materials accumulated ; and the reflec- 
tive abstraction by which this is effected must not only 
follow the laws of Logic, but is most powerfully cultivated 
by the habits of logical study." 

Aristotle has defined Inference as "a thought or propo- 
sition in which, from something laid down and admitted, 
something distinct fi:om what we have laid down follov^^s of 
necessity." But this definition, though it describes the 
Syllogism accurately, seems at first to be inapplicable to 
Immediate Inference, in which, as there is only one premise, 
and as the act of Pure Thought through which we reason 
cannot add any new Matter (that is, any new Intuition or 
Concept), it would appear that the Conclusion cannot con- 
tain anything distinct from what has already been laid down. 



152 THE DOCTRINE OF IMMEDIATE INFERENCE. 

And this Is true ; it cannot contain any new Matter, but it 
may represent tliis Matter under a new Form, so that the 
Conclusion and the Premise will be perfectly distinct Judg- 
ments. Thus, in the instance just given, " quadruped " 
and " rational " are the only Terms that appear in either 
of the two Conclusions, " irrational " being only the equiv- 
alent of " non -rational " ; and both of these are contained 
in the Premise. And yet the Inference is not a mere 
repetition, but the Judgments which it involves are new 
and distinct from what was previously laid down ; for one 
of them is affirmative, while the Premise is negative ; and 
the other denies a certain Mark of any " rational thing," 
while the Premise denies a certain other Mark of any 
" quadruped." If it be argued ftirther, that such Conclu- 
sions are virtually contained in the Premise, inasmuch as 
they become evident to any one who fully apprehends it, 
the answer is, that this is true of all Reasoning, even of 
Syllogisms and Inductions. That a certain step is obvious 
and easily taken, is surely no proof that it is no step at all, 
or that we can get along without taking it. 

1. ^QUIPOLLENCE OR InFINITATION. 

The first sort of Immediate Inference which we have to 
consider is that which the Greek logicians called laoBwa/jLta^ 
and the Latins, ^quipollence ; its more appropriate name 
is Infinitation. It has already been said, that every pair 
of Concepts, such as A and not-A, of which one is merely 
the Contradictory or the privative of the other, divide the 
universe between them. According to the axiom of Ex- 
cluded Middle, either A, or its Infinitated correlative, not- 
A, must belong to everything, and must include everything ; 
and according to the axiom of Non-Contradiction, the pres- 
ence of one in any given case insures the exclusion of the 
other. Hence arise a number of Immediate Inferences, 



^QUIPOLLENCE OR raFINITATION. 153 

some of which are of frequent occurrence in our ordinary 
processes of thought. As already remarked, a negative 
Judgment can always be changed in Form to an affirma- 
tive, or an affirmative to a negative, simply by Infinitating 
one of its Terms, or by dropping its Infinitation ; and the 
result is a new Judgment, the truth of which is an Imme- 
diate Inference from the truth of the antecedent Judgment 
whence it was derived. Here the Inference is only an 
application of the well-known grammatical rule, that two 
negatives cancel each other, and thus become equivalent to 
an affirmative. But the idiom of every language sanctions 
a greater or smaller number of exceptions to this general 
rule, none of which, however, are admissible in Logic, 
where every negation must be construed rigorously. 

The following memoriter lines, which I copy from Bur- 
gersdyck, enumerate the more frequent forms of sequipol- 
lence and of the idiomatic force of negative expressions ; 
but of course, all of them do not hold o;ood in this meaning 
in any other language than the Latin. 

Non omnis = quidam non ; omnis non quasi nullus. 

Non nullus = quidam ; sed nullus non valet omnis. 

Non aliquis = nullus ; non quidam non valet omnis. 

Non alter =: neuter; neuter non jorcssto^ uterque. 
In all cases of Immediate Inference by Infinitation, the 
dependence of the Conclusion upon the Premise is so obvi- 
ous, and so directly governed by the Primary Axioms of 
Pure Thought, that no mistake is likely to arise, except 
fi'om a momentary doubt as to the position or the proper 
force of the negative particle. The two following rules 
comprehend at least all the more important cases, and 
they hold true, I believe, without exception, for the four 
Propositional Forms which are recognized in the Aris- 
totelic system. 

Rule I. To change the Infinitation of the Predicate 

(either by Infinitating it, or by dropping its Infinita- 
7* 



154 THE DOCTRINE OF IMMEDIATE INFERENCE. 

tion), change the Quality of the Judgment; — the 
Quantity of the Judgment then remains unaltered. 
Rule II. To change the Infinitation of the Subject, 
convert the Judgment (i. e. make the Subject and the 
Predicate change places with each other), and then 
either change the Quality, or change the Infinitation 
of the (old) Predicate also; — here, also, the Quantity 
of the Judgment remains unchanged. 
The following are instances, both in the abstract and the 
concrete, of the application of these two Rules to all four 
of the fundamental Judgments, A, E, I, and O, and also 
to their Infinitated forms, here designated as A', E', I', 
and O'. This enumeration was first made out by Mr. 
DeMorgan. It will be seen that it contains no instance of 
mere Conversion, as the cases under that head will be after- 
wards separately considered. To avoid a confusing repeti- 
tion of the negative particle not^ words compounded with 
the negative prefixes un and in have been adopted when- 
ever it was practicable. For the same reason, right is used 
for not-wrong; brutes for not-men; pitiless for not-compas- 
sionate ; &c. 

Premises. Conclusions. 

By Rule I. By Rule n. 

A. Every X is Y. =No X is not-Y. = Every not-Y is not-X. 

All metals are fii- ( ='No metal is infusi- j" =A11 infusible things are 
sible. I ble. ( unmetallic. 

O. Some X are not Y. = Some X are notr-Y. = Some not-Y are not not-X. 

Some men are not ( = Some men are piti- ( = Some pitiless beings are 

compassiouate. \ less.* ^ not mere brutes (not-men). 

E. No X is Y. = Every X is not-Y. = Every Y is not-X. 

No avaricious man C = Every avaricious ( = Every happy man is free 
is happy. \ man is unhappy. \ from avarice. 

* Strictly speaking, or according to the rules of Logic, " not-compassion- 
ate" has the same meaning as "pitiless," for it is the contradictory of 
" compassionate." But in common parlance, there is a slight difference in 
the meaning of the two words ; " not-compassionate," like most other epi- 
thets compounded with a negative particle, means, not entire privation of the 
quality, but only the existence of it in a very low degree. 



^QUIPOLLENCE OR INFINITATION. 155 

I. Some X arc Y. = Some X are not not- Y.= Some Y are not not-X. 
Some wrong acts ( = Some wrong acts ( = Some excusable acts are 
are excusable. \ arc not inexcusable. | not right acts. 

A'. Every not-X is ) ,, .^-v T^ -.r ■ -^ 

not-Y >-=No not-Xis Y. =EveryYi8X. 

Every unjust act j = No unjust act is ex- j = Every (truly) expedient 
is inexpedient. | pedient. ^ act is just.* 

O'. Some not-X are>c ^^ „ „ „ ^_ 

not not-Y C ^^ ^*^™® not-X are Y. = Some Y are not X. 

Some invisible things (= Some invisible (= Some tangible things are 
are not intangible. I things are tangible. | not visible. 

E'. No not-Xis not-Y. = Every not-X is Y. = Every not-Y is X. 

No mortal who-is- ( = Every mortal who- ) t-. . i i • • 

, i.^-) ■ \ u ^ ■ ( = Every mortal who-is-m- 
not-a-brute is in- -; is-not-a-brute is >• 1 1 /. • • i . 

,ie- J ui r • C capable-of-sm is a brute, 

capable of sm. ( capable of sin. } ^ 

V. Some not-X are ) Some not-X are not Y.= Some not-Y are not X. 
not-Y. j 

Some invertebrates (= Some invertebrates ^ = Some wingless animals 
are wingless. | are not winged. \ are not vertebrates. 

The Infinitation of the four additional Judgments first 
considered by Sir W. Hamilton cannot with equal facility- 
be reduced to rule. As either Afa or Afa' is a perfect ex- 
pression of the absolute identity of what the two Terms 
denote, either may be deduced by Infinitation from the 
other, and, by the same means, several other less perfect 
expressions of the same identity may be obtained. But of 
these less perfect expressions some may more properly be 
regarded as inferences by Subalternation. Thus, — 

A£a. AU X^are all ) / jjo X is not-Y ) ( Every not-Y is not-X. 

^ ~ ^ : / No Y is not-X V = ^ All X are Y. 



Afa'. All not-X are I l ,-, . v- ^ v I J ah f -i^- 

., Y \ (. Every no^X IS not-Y ) [ All 1 are X. 

All extended are all divisible = All unextended are all indivisible. 

On the other hand, as Ini and Ini' are indefinite expres- 
sions of the partial disagreement of the two Terms, they 

* Some writers upon the theory of morals, who have strenuously main- 
tained that "no unjust act is expedient," have yet been very unwilling to 
admit that "every expedient act is just." Yet the latter proposition is a 
necessary inference from the former. 



156 THE DOCTRINE OF IMMEDIATE INFERENCE. 

yield no inferences by Infinitation properly so called ; 
though, if some be taken in its semi-definite sense, they 
yield a number of unimportant inferences by what Sir W. 
Hamilton calls Integration. 

The following are the more common inferences by In- 
finitation fi'om the two remaining pah's of these four Judg- 
ments. In these it will be observed that the Quantity of 
the Conclusion often diifers from that of the Premise. 



Ifa. Some X are all Y. =r All not-X are not-Y. = No Y is not-X. 

Some curvilinears are ( = All rectilinears are ( = No circular is rec- 
all circulars. 1 not-circulars. 1 tilinear. 



Some not-X are not > 
not-Y. i = 



Am. No X is some Y. .j ^ ^ ^ == Some Y are not-X. 



No tyrants are some (= ^""^^ ^'.^°, ^^^ °°*? = Some kings are 
kings. i Sro°yal '' I not.tyrannical. 

Ifa'. Some not-X are all ) ,.. _^ . , _^ ( = Some not-X are 

. V V = No X is not-Y. J. ^ V 

not-Y. ^ I not Y. 

Some unsentient are ( == No sentient thing is ( = Some unsentient 
all inorganic. ^ inorganic. \ are not organic. 

Ani'. Not any not-X is^r- v xv o ..vv 

•^ .-v h = Some X are not Y. = Some not-Y areX. 

some not-Y. ^ 

Not any dishonest is ( = Some honest are not ( = Some imprudent 
some imprudent. \ prudent. ( are honest. 

2. Conversion. 

A Judgment is said to be converted when its Subject 
and Predicate have been made to change places with each 
other. Before Conversion, the Judgment is called the 
Convertend ; after Conversion, it is the Converse. The 
logical doctrine of Immediate Inference by Conversion 
shows us when and why the truth of tlie Converse is a 
necessaiy consequence of the truth of the Convertend. 
In other words. Logic takes notice only of what is called 
illative Conversion, in which the Convertend and the Con- 
verse must either both be true, or both be false, together. 
Thus, the Conversion of No A is B, into No B is A, is illa- 
tive ; we can say, 



CONVERSION. 157 

No carnivorous animal is ruminant ; 

therefore^ No ruminant animal is carnivorous. 
But the Conversion of Some A are not J5, into Some B are 
not A^ is not illative ; because we can say, Some men are not 
logicians^ it does not follow that Some logicians are w)t men. 

In Conversion of Judgments, the learner must remem- 
ber that the whole Predicate must change places with the 
whole Subject; — that is, whatever belongs to the Predi- 
cate must be transfeiTed to the Subject's place, and what- 
ever relates to the Subject to the Predicate's place. For 
example ; — Some temple is in the city^ is not converted into 
Some city is in the temple, but into Something in the city is 
a temple. Again, — the Predicate of Every old man has 
been a hoy, is not boy, but has been a boy ; therefore, it is 
not converted into Some boy has been an old man, but into 
Some one who has been a boy is an old man. To avoid mis- 
takes of this sort, every proposition, before Conversion, — 
or, indeed, before it is subjected to any logical treatment 
whatever, — should be reduced to its simplest logical form, 
— that is, to the formula A is B, or A is not B. Then no 
error can arise, if we remember that all which precedes the 
Copula, is or is not, is the Subject, and that all which fol- 
lows the Copula is Predicate. 

In treating of Conversion, as well as in other portions of 
the subject, we first consider exclusively the doctrine of the 
Aristotelic system, which admits only of four fundamental 
Judgments, and reserve for subsequent treatment the 
Hamiltonian theory of eight Judgments. 

There are three sorts of Conversion. The first is appli- 
cable to £j and I, Universal Negatives and Particular 
Affirmatives, and is called Simple Conversion, because both 
tlie Quantity and the Quality of the Judgment remain un- 
changed ; that is, E is converted into E, and I into I. K 
it is time that No man is immortal, it follows by Immediate 
Inference that No immortal is man; for if any one immor- 






158 THE DOCTRINE OF IMMEDIATE INFERENCE. 

tal were a man, it would not be true that No man is irro- 
tnortal. Likewise, if Some men are just, it follows imme- 
diately that Some just beings are men ; because the assertion 
that No just being is a man, would contradict the Con- 
vertend. By Simple Conversion, then, a Universal Nega- 
tive passes over into a Universal Negative, and a Particular 
Affirmative into a Particular Affirmative. 

The second sort is Conversion per accidens, in which the 
Quantity is changed from Universal to Particular, but the 
Quality remains unaltered. This is applicable to A, and 
also may be applied to E, though the latter, as we have 
just seen, may also be converted simply. But A cannot 
be converted simply ; because, though all men are animals, 
it does not follow that all animals are men. The Judgment 
in the Convertend is, that men are mcluded under the class 
of animals, not that they constitute all animals ; they are 
only some animals. Hence the Converse is. Some animals 
are men. We have already seen that E is converted sim- 
ply into E ; but O also is obtained by Immediate Inference 
from E; for, if None are, it follows that Some are not. 
Hence, the Convertend, No man is immortal, yields as its 
Converse, not only E, No immortal is man, but O, /Some 
immortals are not men. Conversion per accidens, then, 
changes A into I, and E into O, the Quantity in both 
cases being diminished, but the Quality remaining im- 
changed. 

The Judgment O remains, and this cannot be converted 
either simply or per accidens. From the Convertend, 
8ome men are not learned, we cannot infer that Some 
learned beings are not men. Indeed, properly speaking, 
O cannot be converted at all on the Aristotehc system ; 
but by an artifice which is called Contraposition, the third 
sort of Conversion, another Judgment can be mferred 
from it, which is called its Converse, though it is prop- 
erly the Converse of its ^Equipollent or Infinitated equiv- 



CONVERSION. 159 

alent. In order to convert hj Contraposition, then, first 
infinltate the Convertend by Rule First, and then convert • 
simply. Thus, — 

Couvertend. Some A are not B. Some men are not learned. 

Infinitated equivalent. Some A are not-B. Some men are unlearned. 
Converse of this. Some not-B are A. Some unlearned persons are men. 

Hence I is the Converse by Contraposition of O ; and 
in like manner, A by Contraposition yields S, the effect 
of this sort of Conversion being to change the Quality of " 
the Convertend, while its Quantity remains unaltered. A 
is thus contraponed : — 

Convertend. AU A is B. All men are rational. 

Infinitated equivalent. No A is not-B. No man is irrational. 

Converse of this. No not-B is A. No irrational being is a man. 

No inference can be obtained fi-om I by Contraposition ; 
for if infinitated, I becomes O, which cannot be converted 
except by infinitating it back again. Logicians seem to 
have overlooked the fact that £! can be contraponed into 
I, though the inferred Judgment in this case, because its 
Quantity is diminished, is weak and comparatively worth- 
less. Thus, — 

No A is B. No fish is warm-blooded. 

Every A is not-B. Every fish is cold-blooded. 

Some not-B are A. Some cold-blooded animals are fishes. 

The results of the three sorts of Conversion have been 
summed up in this (nonsense) mnemonic line, in which 
each dissyllable contains the vowel-symbol first of the Con- 
vertend and then of its Converse; and each pair of these 
dissyllables is followed by the (italicized) abbreviation of 
the kind of Conversion by which the two preceding infer- 
ences have been obtained ; simp. = Simple : Ace. = per 
accidens ; and Cont. = Contraposition. 

Ecce tibi, simp. ; armi-geros, ace. ; ante boni, Cont. 
The same thing is more briefly indicated in these two 
Latin words, Hoc capessit, in which oc-ca signifies that O 
and A are converted by Contraposition; ape, A and Ejoer 
accidens ; essi, E and I simply. 



160 THE DOCTRINE OF IMMEDIATE INFERENCE. 

The most striking merit of Sir W. Hamilton's system of 
the thorough-going quantification of the Predicate is, that 
it abohshes at once this whole cumbrous system of Con- 
version in three kinds, with its attendant rules, and sub- 
stitutes for it the universal and self-evident process of Sim- 
ple Conversion. As it has already been demonstrated, that 
each Term of every Judgment has its own Quantity in 
Thought, and consequently, that the distinction of Subject 
and Predicate may be, for most logical purposes, left en- 
tirely out of view, every Judgment being reduced to an 
equation, in which, of course, it makes no difference which 
of the equated quantities is placed first. Conversion be- 
comes at once a simple, uniform, and self-evident process. 
As an old logician (Du Hamel, as quoted by Mr. Baynes), 
remarks, " omnes conversionum leges pendent a cohaesione, 
vel potius ab identitate, subjecti et attributi ; quod si enim 
subjectum conjmigitur et identificatur, ut aiunt, cum attri- 
buto, necesse est pariter attributum uniri et identificari 
cum subjecto." Though it is hardly necessary even for 
the youngest learner, I give examples of the Hamiltonian 
mode of converting each of the eight Judgments. 

Converted, Converse. 

Afa. All rational are all moral ( = Afa. All moral are all rational 

beings ( beings. 

Afi (A). All lilies are (some) fra- ( = Ifa. Some fragrant things are all 

grant ( lilies. 

Ifii. Some plants are all trees = Afi. All trees are (some) plants. 

Ifi (I). Some vicious men are ricli = Ifi. Some rich men are vicious. 

,-^^ -k-r .^ -^ ,«C=Ana. Nothing that can move itself 

Ana (B). No matter can move itself j .^ j^^^j^j. 

Ani. Not (any) indistinct are ( = Ina. Some sounds are not indis- 

some sounds \ tinct. 

Ina (O). Some virtuous men are j = Ani. Not (any) happy are soma 

not happy ( virtuous men. 

Ini. Somesingersarenotsomc ( = Ini. Some musicians are not 

(good) musicians ^ some singers. 

Conversion per accidens^ says Mr. Mansel, is so called 



CONVERSION. 161 

because it is not a Conversion of the Universal per se, but 
only of the Particular which happens to be included in the 
Universal. " Some B is A," is primarily/ the Converse of 
" Some A is B," and only secondarily of " All A is B," or 
because " All A " includes " Some A." Properly speak- 
ing, then, it is no Conversion at all, but only an Immediate 
Inference by Subalternation from the proper Converse. 
This is clearly seen in the case of the Universal Negative, 
Ij ; No A is B, is first converted into E, No B is A, whence 
we obtain by Subalternation O, Some B are not A. 

Moreover, it is evident that, by reconverting the Con- 
verse, we ought to regain the Convertend. But this can- 
not be done after converting per accidens ; we first convert 
A into I, and then reconvert I, not into A, but into I. 
For example ; — All men are mortal^ yields by accidental 
Conversion, Some mortals are men; and this is reconverted 
simply into Some men are mortals. 

It is further argued by Hamilton, that the Aristotelic 
doctrine applies Conversion to the naked Terms only, — 
to the Subject and Predicate of the Convertend without 
regard to the Quantity of either; it thus changes all to 
some, and, as we have just seen, it makes the total Quan- 
tity of the Converse inferior to that of the Convertend. 
But this is evidently wrong ; for the quantified Terms are 
the Concepts which were compared in Thought in the 
Convertend, and these only ought to appear after Conver- 
sion, and appear unchanged. Contraposition, as we have 
ali'eady shown, is a mediate process, the Conversion being 
possible only through a previous Infinitation ; for the origi- 
nal Judgment, on the Aristotehc doctrine, is not convert- 
ible at all. But as every Judgment is certainly the result 
of a comparison, to assert that it is inconvertible, is to 
maintain that A can be compared with B, while, at the 
same moment, B is not compared with A ; — which is 
absm'd. Comparison is necessarily bilateral. 



162 THE DOCTRINE OF IMMEDIATE INFERENCE. 

3. Opposition and Integration. 

Opposition is said to exist between Judgments which 
have the same Matter (i. e. the same naked or unquanti- 
fied Subject and Predicate), but differ in Quantity, or in 
Quahty, or in both. The logical doctrine of Opposition 
sliows us what can be immediately inferred as to the truth 
or falsity of one Judgment, from positing or sublating 
(i. e. affirming or denying) one of its Opposites. Thus, 
from positing E, JVb A is B^ I can immediately infer the 
truth of its Subaltern Opposite, O, Some A are not B^ and 
the falsity of its Contradictory Opposite, I, Some A are B ; 
but I cannot infer, from sublating El, the truth of its Con- 
trary Opposite, A, All A are B. 

But here the word Opposition must be taken in a tech- 
nical and qualified sense. It was first appHed only to the 
relations between two Contraries, or two Contradictories j 
and this is its proper or strict meaning, as any two such 
Judgments are opposed to each other, the one negativing 
the other, and it is impossible that the two should be true 
together. But as it was convenient for Logicians to con- 
sider the relations of Subalternation and Sub-Contrariety 
under the same head with the two former, the meaning of 
the word was extended so as to cover all the relations 
existing between two Judgments of the same Matter, but 
of different Form, although some of these are relations not 
of opposition, but of congniity. 

There are four sorts of Opposition. The first and most 
perfect of these is that of Contradiction^ which exists be- 
tween two Judgments which differ from each other hath in 
Quantity and Quality ; that is, between A and O, and be- 
tween £j and I. This sort of Opposition is governed by 
the Axiom of Excluded Middle, which declares that of 
two Contradictories, — that is, of two Judgments between 
which there is no "Middle," no intermediate Judgment, — 



OPPOSITION AND INTEGRATION. 163 

one must be true ; and then the Axiom of Non-Contra- 
diction adds, that the other must be false. Now, A and 

are two such Judgments, and hkewise E and I ; so also 
the two Suigular Judgments, Socrates is wise, and Socrates 
18 not wise. Between either of these pairs, no " third " or 
intermediate Judo-ment is conceivable. Hence the univer- 
sal rule for this sort of Opposition, that Contradictories can- 
not both he true, and cannot both be false. Therefore, as 
both cannot be true, if I posit (affirm) one, I immediately 
infer that the other is sublated (denied) ; and as both can- 
not be false, if I sublate one, the other is posited. For 
example ; — if E is not true, that No quadruped is ratioiial, 

1 must be true, that Some quadrupeds are rational. 

Observe that two Judgments properly contradict each 
other only when that which is affirmed by the one is de- 
nied by the other, — 1. in the same manner ; 2. in the same 
respect; 3. in the same degree; and 4. at the same time. 
Thus, to borrow some examples from Aldrich, — 1. A dead 
body is, and is not, a man ; that is, it is a dead man, but 
not a living one. 2. Zoilus is, and is not, black ; that is, 
black-haired, but red-faced. 3. Socrates is, and is not, 
long-haired ; that is, he is so, if you compare him with 
Scipio, but is not so, if you compare him with Xenophon. 
4. Nestor is, and is not, an old man, according as you 
speak of him when in childhood, or when he was at the 
siege of Ti'oy. 

The second sort of Opposition is that of Contrariety, 
which exists between two Universal Judgments, that differ 
in Quality, but are alike in Quantity ; that is, between A 
and E. Here the Axiom of Excluded Middle does not 
apply ; for between A and E, there is a " Middle " or 
intermediate Judgment, namely, I. Though it is not true, 
either that all men are wise, or that no man is wise, it is 
true that some men are wise. Hence both Contraries may 
be false, so that I cannot infer the truth of one from the 



164 THE DOCTRINE OF IMMEDIATE INFERENCE. 

falsity of the other. On the other hand, as one of these 
Contraries affirms what the other denies, the Axiom of 
Non-Contradiction apphes ; both Contraries cannot be true ; 
and, therefore, from the truth of one I can immediately 
infer the falsity of the other. Accordingly, the nile is, 
Contraries may he false together, hut hoth cannot he true. 
Therefore, fi'om positing either A or E, I can immediately 
infer that the other is sublated ; but from sublating either, 
I cannot infer that the other is posited. 

The tliird sort of Opposition is that of Svh-Oontrariety, 
which exists between two Particular Judgments, that differ 
in Quality, hut are alike in Quantity ; that is, between I 
and O. To these, the Axiom of Excluded Middle is 
applicable ; for there is no third, or intermediate. Judgment 
conceivable between Some are, and Some are not. Accord- 
ingly, both cannot be false, but one must be true. On the 
other hand, if I and O are considered as Propositions, that 
is, if the Judgments are expressed in words, the Axiom of 
Non-Contradiction does not apply to them ; for both may 
be true. Though some men are learned, it is also true that 
some men are not learned. But observe, that the " some 
men " in the latter case are not the same " some men " as 
in the former ; though expressed by the same words, they 
are thought as different. To make the former Proposition 
true, " some men " may be thought to be " graduates of 
Oxford " ; to make the latter true, " some men " may 
mean " American Indians." As Propositions, then, and 
possibly as Judgments, the two assertions do not contradict 
each other, but may both be true. Hence the rule, that 
Suh- Contraries may he true together, hut cannot hoth he false. 
Therefore, by sublating either I or O, we immediately infer 
that the other is posited ; but by positing either, we can- 
not infer that the other is sublated. Of course, Sub- 
Contraries can be called " opposites " only in a qualified 
and technical sense ; they are actually congruent, or, to 



OPPOSITION AND INTEGRATION. 165 

adopt one of Hamilton's newly-coined words, tliey are 
" compossible." 

The fourth sort of Opposition is that of Subalternation^ 
which exists between Judgments alike in Quality, hut dif- 
ferent in Quantity ; that is, between A and I, and between 
E and O. Here, again, it is evident that the " Opposi- 
tion " is merely technical, the two Judgments being not 
merely consistent, but so nearly allied that the Particular 
can be inferred from its Universal by the Axiom of Iden- 
tity. Since all includes some^ if we affirm A, All A are B^ 
we thereby also affirm I, Some A are B ; and in like man- 
ner, to posit El is also to posit O. The same Axiom com- 
pels us to think, that sublating I sublates A also, and 
sublating O sublates S also. In this sort of inference, the 
Universal may be called the Suhalternans, and the Particu- 
lar, the Subalternate. Hence we have this rule for infer- 
ence by Subalternation, that if the Suhalternans is true, the 
Subalternate is true also ; and if the Subalternate is false, 
the Suhalternans is false also. 

Summing up, we have the following list of Immediate 
Inferences by Opposition. 

j If A is true, O is false, £! false, and I true. 

( If E is true, I is false, A false, and O true. 

I If I is false, E is true, O true, and A false. 

( If O is false, A is true, I true, and E false. 

If A is false, O is true, ) ^i ,i •, 

. . \ the others unknown. 

It E is false, I is true, ) 

If I is true, E is false, ) ,i .i i 

' . p 1 f fhe others unknown. 
If O is true, A is false, ) 

Hence it appears, that from the truth of a Universal or 
the falsehood of a Particular, we may infer the character of 
all the opposed Judgments ; but from the falsehood of a 
Universal or truth of a Particular, we can know the char- 
acter only of the Contradictory. 



I 



166 



CONSPECTUS OF THE DOCTRINE OF 



JUDGMENTS, considered 
in reference to 
Quantity, are either Univer- 
sal or Particular ; to 
Quality, are either Affirma- 
tive or Negative ; to 
Quantity and Quality, are 
of four sorts : — 



Affirmative Predesignations of Univer. 
sal Judgments. 

All — Every — Each— This — That 
— These — Those — a Proper 
Name. 

A. Universal Affirmative. 

e. g. All X is Y. 

All metals are lustrona. 



IMMEDIATE INFERENCE proceeds 

BY InFINITATION 

of the Terms of a Judgment, or by dropping their Infini- 
tation, the Judgments thus produced being, in certain 
cases, cequipollenty or equivalent to those from which 
they were derived. 



BY Opposition, 

or the relation that 
exists between Judg 
ments which have 
the same naked or | 
unquantified Subject I 
and Predicate, but "" 
differ in Quantity, 
or Quality, or both. 




Sub-Contrary. 



Four Kinds 

1. Contradiction 
exists between Judgments 
which differ both in Quan- 
tity and Quality. 
Rule. — Contradictories can- 
not both be true and cannot 
both be false. Hence, 
to posit A is to sublate O 
« E " " I 
to sublate A is to posit O 
" E " " I 

and conversely, 

to posit O is to sublate A 
&c. 



BY Conversion, 

or causing the Subject and 
Predicate of a Judgment 
to change places with each 
other, but in such man- 
ner that if the Convertend 
is true, then the Converse 
will be true also. 



Three Kinds 

1. Simple, E & I, 

without changing either the Quantity 

or the Quality. (Ecce-tihi.) 
Convertend. No X is Y. E into 

Converse. No Y is X. E. 

Convertend. Some X are Y. I into 
Converse. Some Y are X. I. 



i 



JUDGMENTS AND IMMEDIATE INFERENCE. 



167 



Negative Predesignations of Univer- 
sal Judgments. 

None — Not any — Not one — Not 
this — Not that — " Not " prefixed 
or suffixed to a Proper Name. 



Predesignations of Particular Judg- 
ments, either Affirmative or Nega- 
tive. 

Some — Not all — or any indication 
of an indefinite part of a whole. 



E. Universal Negative. 

No X is Y. 

No quadruped is rational. 



I. Particular Affirmative, 

Some X are Y. 
Some swans are black. 



O- Particular Negative. 

Some X are not Y. 
Some men are not fa- 
mous. 



Two Kinds of Infinitation. 



Rule. — To change the Infinitation of 
the Predicate, either by infinitating 
it or by dropping its Infinitation, 
change the Quality of the Judg- 
ment ; the Quantity of the Judg- 
ment remains unaltered. 



Rule. — To change the Infinitation of 
the Subject, convert the Judgment, 
and then either change the Quality, 
or change the Infinitation of the 
(old) Predicate also. Here, also, 
the Quantity is unaltered. 



OF Opposition. 



2. CONTRARIETT 

exists between Universal 
•Tudgmentg that differ in 
Quality, but are alike in 
Quantity. 
Rule. — Both Contraries may 
be false, hut both cannot 
be true. Hence, 
to posit A is to sublate E 
" E " " A 



3. SUB-COKTEARIBTT 

exists between Particular 
Jud<;ments that differ in 
Quality, but are alilie in 
Quantity. 

Rule. — Sub-Contraries may 

both be true, but cannot 

both be false. Hence, 

to sublate I is to posit O 

" O " "I 



4. SUBALTEBNATIOM 

exists between Judgments 
alike in Quality, but differ- 
ent in Quantity. 

Rule. — If the Subalternana 
(the Universal) is true, the 
Subalternate (the Particu- 
lar) is also true ; and if the 
Subalternate is false, the 
Subalternans is false also. 
Hence, 

to posit A is to posit Z 

" E " " O 

to sublate I is to sublate A 

»i Q U ME 



OF Conversion. (^JSbc eapessit.') 



2. Per Accidens, A & E, 

changing the Quantity, but not the 

Quality. (Armi-geros.) 
Convertend. All X is Y. A into 

Converse. Some Y is X. I. 
Convertend. No X is Y. E into 

Converse. Some Y is not X. O. 



3. Bt Conthaposition, a & O. 

changing, not the Quantity, but the 
Quality, through infinitating the 
Predicate. (Ante-boni.) 

Convertend. All men are mortal. A. 

Converse. No immortal is man. E. 

Convertend. Some men are not 

white. O- 

Converse. Some not-white are men. I. 



168 



THE DOCTRINE OF IMMEDIATE INFERENCE. 




Sub-Contrary 



That the various points in the doctrine of this sort of 
Immediate Inference might be more easily remembered, 

the old logicians contrived, 
not some mnemonic verses, 
as on other occasions, but 
the accompanying inge- 
nious diagram, which may 
be called the Square of 
Opposition. It is very 
easy to retain the whole 
theory in the memory, 
when we observe the 
proper position, upon this 
square, of the vowels which 
indicate the four species of Judgments. The upper hne 
belongs to the Universals, A and E ; the lower line to the 
Particulars, I and O ; the left hand to the Affiraiatives, 
A and I ; and the right to the Negatives, "E and O. Then 
it is easily remembered, that the two diagonals represent 
Contradiction, the upper line Contrariety, the lower one 
Sub-Contrariety, and each of the two sides Subalternation. 
For the further convenience of learners, I have brought 
together in the preceding Conspectus the principal techni- 
calities and rules in the Aristotelic doctrine of Judgments 
and Immediate Inference. 

Hamilton has considerably enlarged and modified the 
doctrine of Immediate Inference by Opposition, by intro- 
ducing, what the logicians had hitherto neglected, the 
semi-definite meaning of some, — that is, some at most, — 
some excluding all and none. In the Aristotelic doctrine, 
some was applied exclusively in its wholly indefinite mean- 
ing, as some at least, — some, perhaps all; — and in nega- 
tives, some, perhaps none. Yet, as Hamilton remarks, some 
is always thought as semi-definite when the other Term 
of the Judgment is Universal ; and it is only when both 



OPPOSITION AND INTEGRATION. 169 

Terms are Particular, that the some of each is left wholly 
indefinite. Thus, when we say. Some men are (all) hlacTc, 
we mean to deny that all are black ; Some fioivers are not 
(any) fragrant^ denies that Twne are fragrant. 

But in the case of Subalternation, which Hamilton pre- 
fers to call Restriction, if we introduce this semi-definite 
meaning, and think some as some only — not all, instead of 
having an Inference from the Subalternans to the Subalter- 
nate, we find a true Opposition between them ; to adopt 
the Hamiltonian word, the two Judgments are Ineompos- 
sible. Thus, Some (only — not all) men are yellow, is really 
opposed to All men are yellow, instead of being an Infer- 
ence from it ; and in hke manner. Some (not all) bipeds 
are not men, is opposed to No bipeds are men. This new 
sort of Opposition or Incompossibility, as it exists between 
two Judgments which are alike in Quality, either both 
Affirmatives or both Negatives, while the other two sorts. 
Contradiction and Contrariety, differ in Quality, is called 
Inconsistency. Of course, as two Inconsistents, like any 
other two Incompossibles or Opposites, cannot both be 
true, the true Inference is, that by positing either A or I, 
E or O, the other is sublated. To express the whole doc- 
trine of Subalternation or Restriction in one rule ; — If 
some means some — perhaps all, the Subaltemate is a direct 
Inference from positing the Subalternans ; but if some 
means some — not all, the Subalternans and Subalternate 
ai"e Opposite or Incompossible, so that, by positing either, 
the other is sublated. 

Again, it has already been shown that Sub-Contrariety 
is properly no Opposition at all, so that both Judgments 
may be true ; though, as both cannot be false, sublating one 
enables us to posit the other. But if we introduce the 
semi-definite meaning of some here also, we have a new 
Inference from one to the other ; — from the one some, 
which is a part, to the other some, which is the remaining 
8 



170 THE DOCTRINE OF IMMEDIATE INFERENCE. 

part necessary to constitute the wliole. This sort of Infer- 
ence Hamilton would call Integration, as its effect is, after 
cletermming one part, to reconstitute the wliole by bringing 
into view the remaining part. Thus, if I know that Some 
(not all) men are white, I can immediately infer that Some 
(other) men are not white ; and if Some poets are not philos- 
ophers, it follows that Some (other) poets are philosophers. 
In such cases, though the two Judgments are different in 
Quahty, they are not opposed, but congruent ; and the 
Inference may be not only to all others definitely, but to 
some others indefinitely. It is valid, also, whether some 
appears in the Subject or Predicate. Thus, from Men are 
some animals, we immediately infer that Men are not some 
(other) animals (say, brutes). Here, the Inference con- 
cerns the Predicate, while in the preceding cases it con- 
cerned the Subject. 

To apply the whole doctrine of Incompossibility and In- 
tegration, in both meanings of the word some, to the eight 
Hamiltonian Judgments, is evidently a long and complex 
process. The following table (page 172), in which the 
whole process is worked out, is borrowed from Sir William 
Hamilton, and placed here, not, of course, that it may be 
committed to memory, but because the examination of it 
will be a useftil exercise for the learner. In explanation 
of it, observe that the Incompossibility, or the fact that the 
two Judgments cannot both be true, — and in some cases, 
the Restriction (Subalternation) and the Integration, — 
may be bilateral (here marked hi^, as affecting both Subject 
and Predicate ; thus, 

All physical laws are all efficient causes. 
Not any physical law is any efficient cause. 
Or unilateral (un), as affecting either the Subject only 

thus, 

All men are all rational. 

Some men are not (any) rational. 



OPPOSITION AND INTEGRATION. 171 

Or the Predicate only; thus, — some in the second Judg- 
ment being semi-definite, — 

All dogs are all barking animals. 

All dogs are some barking animals. 
Or it may be unilateral cross (un. cr.), as reversing in 
the one Judgment the relation of Genus and Species — 
containing and contained — which exists between the 
Terms of the other Judgment ; thus, some being semi- 
definite, 

All whites are some civilized. 

Some whites are all civihzed. 
Or bilateral cross (hi. c/.), as affecting both Terms, but in 
opposite relations, — as fi'om Particular to Universal in 
the Subject, and from Universal to Particular in the Predi- 
cate ; thus, some being semi-definite. 

Some blacks are all Africans. 

Not any black is some Africans. 
Or bilateral direct (hi. di.^, as affecting both Terms, and 
excluding any intermediate or third Judgment, both propo- 
sitions remaining the same after conversion ; thus, 

Some men are (some) irrational. 

Not any man is (any) irrational. 



r 



172 



THE DOCTRINE OF IMMEDIATE INFERENCE. 



TABLE 

OF THE Mutual Relations of the Eight Propositional Forms ok 
EITHER System of Particularity. {For Generals only.) 



A 

a 
a 

B 

■S . 

m 

Hi 
1 

c 
S 
(k 

S 
i 


m5 


Restr. bi. 

Restr. «M. 
Restr. un. 


Restr. bi. 

Restr. un. 
Restr. un. 


Res. & Int. bi. 
Integr. un. 
Res. & Int. un. 

Integr. un. 
Res. & Int. un. 

Res. & Int. un. 
Res. & Int. tin. 
Integr. bi. 


il 

Is 


8 8.^ a a 

S S.O 8 S 


8 a..i 8 8 
S S.O s s 




Restr 
Restr 
Restr 

Restr 
Restr 


Restr 
Restr 
Restr 

Restr 
Restr 


ft 

^1 


eq CO ■* ■* tK 

III II 

i-l r-l rH IN CO 


CO !■* 00 00 00 
III II 

»o lo lO so t- 


1—8 
2—6 
2—8 

3—7 

3—8 

4—6, 6—4 
4—7, 7—4 
4—8, 8—4 


a 

^ o 
H c 

a 3 a> 
^ S 

t-i A 




Incons. tin. 
Incons. un. 

Incons. un. cr. 


Incons. un. 
Incons. un. 

Doubtful, cr. 


Contrar. bi. 
Contrar. un. 
Contrar. un. 

Contrar. un. 

Contrar. bi. cr. 

Contrar. un. 
Contrar. bi. cr. 

Contrar. bi. di. 


■g's 

■gs, 

"o g 




o 


Contrar. bi. 
Contrar. un. 
Contrar. tin. 

Contrar. un. 

Repugn, bi. cr. 

Contrar. un. 
Repugn, bi. cr. 

Repugn, bi. di. 


•a 

ci J) 
= it a 

° ■- o 

i.S2 


> 


m7777 

t£ (£r cS en cc -j 


Ana — Ani 
Ana — Ina 
Ana — Ini 
Ani — Ina 
Ani — Ini 
Ina — Ini 


1 1 1 1 1 II II 1 1 i 1 1 II 


SS3 
■^ o 


Affirmat. 
1—2 
1—3 
1—4 
2—3 
2—4 
3-4 


Negat. 
5—6 
5—7 
5—8 
6—7 
6—8 
7—8 


h2iO<r>t~0ClOCDt^00lOCOt-00lOCOl»00 

S 1 M 1 1 1 1 1 1 II 1 1 1 M 

^i-lr-CrHr-itqNNiMCOCOCOCOl"-*-*-* 



Abbreviations : Contrar. = Contraries ; Incons. = Inconsistents ; Int. or Integr. =■ 7n- 
tegration ; 'Repxisn. = Repugnants, Contradictories; Kes. or 'Restr. = Restriction, Sub- 
alternation ; Blanks, in I = Compo.tsibles ; in 11. = No inference. 

This Table may nut be quite accurate in details. 



i 



OPPOSITION AND INTEGRATION. 173 

It appears from this Table, that Afi and Ina (A and O), 
which, on the Aristotelic doctrine, are Contradictories, be- 
come only Contraries when we admit the semi-definite 
meaning of some ; for by sublating iwa, which denies only 
a part (some only)^ we know not whether to posit Afi^ 
which affirms the whole, or Iji^ which affirms only some 
(other) part, or Ana^ which denies the whole ; since each 
of these three is incompossible with Ina. For the same 
reason. If a and Ani^ which are only A and O converted, 
are merely Contraries on this system, though Contra- 
dictories on the other, wherein some means perhaps all. 
Indeed, there can be no Contradiction on this system, 
wherein whole and part negative each other, just as much 
as affirmation and negation. The only Contradictories are 
those in which the distinction of whole and part does not 
exist ; — Judgments about Singulars or Individuals, for 
, instance, and ■ about Universals regarded as Singulars or 
as undivided wholes. Thus, Common salt is chloride of 
sodium contradicts Common salt is not chloride of so- 
dium; for Common sa% though really a General Term, 
is here actually thought as undivided, so that the two 
Judgments contradict each other as directly as do these 
two Singulars, — John is sick^ John is not sick. If either 
Judgment in one of these pairs is sublated, the other is 
necessarily posited. 

"The propositional form Ifi is consistent with all the 
affirmatives ; Ini is not only consistent with all the nega- 
tives, but is compossible with every other form in uni- 
versals. It is useful only to divide a class, and is 
opposed only by the negation of divisibility." 

The whole scheme of Opposition upon this system may 
be safely characterized as too complex to be of any prac- 
tical use, though the learner may be profited by some 
study of its details. 



174 MEDIATE INFERENCE OR SYLLOGISM. 



CHAPTER VII. 

THE DOCTRINE OF MEDIATE INFERENCE: THE ARISTOTELIC 
ANALYSIS OF SYLLOGISMS. 

1. Figure and Mood. — 2. Conditional Syllogisms. — 3. Defective and 
Complex Syllogisms. 

MEDIATE Inference is that act of Pure Thought, 
whereby the relation of the two Terms of a pos- 
sible Judgment to each other is ascertained by comparing 
each of them separately with a third Term. Thus, if I 
cannot immediately determine whether A is, or is not, B,^ 
I can compare each with M. If, as the result of such com- 
parison, it is found that A is ilf and B is M, then we infer 
mediately — that is, through this relation of each to a third 
— that A is B. But if this comparison shows that one of 
these Terms is, and the other is not, M, then we infer 
mediately that A is rwt B. The affirmative conclusion is 
evidently governed by the Axiom of Identity, which de- 
clares that A is B, if it is that (M) which is the equivalent 
of B ; or to lise language more consonant with the phrase- 
ology hitherto employed, and converting B is iltf into 31 is 
B, we say that B is a Mark of A, when it is a Mark of 
that (M) which is a Mark of A, — nota notce est nota rei 
ipsius. The negative conclusion results from the Axiom 
of Non-Contradiction, which declares that A is not B, when 
it is equivalent to that (or has for a Mark that) (M), 
which is not B ; or, what is the same thing, when it is not 
equivalent to that (M) which is B. 

The ftindamental principle of Mediate Inference or Syl- 



THE ARISTOTELIC ANALYSIS. 175 

logism is thus traced to those Axioms which, as we have 
already seen, must govern all the processes of Pure 
Thought ; or rather, Mediate Inference itself is but one of 
the special applications of those Axioms. Instead of using 
these Primary Axioms themselves, logicians have usually, 
in order to demonstrate the processes of syllogistic reason- 
ing, preferred to employ certain intermediate principles or 
maxims, one of which we have just mentioned, — that the 
Mark of a Mark vi a Mark of the thing itself. But as these 
maxims can be directly deduced from the original Axioms, 
to which, indeed, they owe all their validity, it seems bet- 
ter to test the legitimacy of each step by a reference to the 
primary, rather than to any derivative, principle. 

Thus far, A and B, in their comparison with M, have 
been regarded simply as undivided wholes ; but it is evi- 
dent that the same considerations will hold good if we sub- 
stitute, for either or both of them, all, or any indefinite part, 
of a divided Universal. Thus, if we find that Some A are 
M, and Some B are M, we are compelled to conclude, by 
the Axiom of Identity, that Some A are (some) B ; or, 
taking a negative instance, if Some A are M, and Not any 
B is 31, then we infer that Some A are not (any) B. 
Hence we see the correctness of the derivative or mter- 
mediate principle which Sir W. Hamilton enounces as 
" the supreme Canon of Categorical Syllogisms," — In so 
FAR AS two Notions (Concepts or Individuals), either loth 
agree, or, one agreeing, the other does not agree, with a com- 
mon third Notion, in so far these Notions do or do not 
agree with each other. But if, by calling it " supreme," he 
means that it is the ultimate and original Canon, his posi- 
tion may be doubted ; for it is evidently a compound 
statement, embracing, with an unimportant change of 
phraseology, the two Primary Axioms of Identity and 
Non-Contradiction, and guarding them with those limita- 
tions under which alone are they ever applicable. 



176 MEDIATE INFERENCE OR SYLLOGISM. 

"We have seen that, though either or both of the two 

Terms be quantified Particularly, the Syllogism still holds 
good, — at least, to the extent to which the two Terms 
are quantified. But the third Term must be taken Uni- 
versally at least once in comparing it with the other 
Notions ; otherwise, we have no security that these others 
are compared with the same, or " a common," third Term. 
Though we know, for instance, that A is some 3f, and B 
is some M, still we cannot conclude that A is B ; for the 
*' some M " which is A may not be the same " some M " 
which is B. Though Some learned men are pedants, and 
^ome learned men are wise, it does not follow that Pedants 
are wise ; for two very different classes of learned persons 
are here spoken of. Hence we have this general rule for 
all Syllogisms, that the Middle Term must he distributed 
(\. e. taken Universally) in at least one of the comparisons 
which are instituted between it and the other two Terms. 
We say, " at least one " of the two comparisons ; for the 
other may be quantified Particularly without injury to the 
reasoning. Thus, if All men are mortal, and X, Y, and Z 
are (some) men, we may legitimately conclude that X, Y, 
and Z are mortals ; for to whatever class these " some men " 
belong, they are necessarily included imder " all men," 
who are declared to be mortal. 

A Syllogism evidently comprises three Judgments, one 
of which affirms the agreement or non-agreement of its 
two Terms with each other to be the necessary consequence 
of two other Judgments, in which a common third Term 
is affirmed to agree with both, or with one only, of these 
two Terms. The main Judgment is called the Conclusion ; 
the two subsidiary Judgments, on which it depends, are 
termed the Premises ; and the necessary connection be- 
tween the Premises and the Conclusion — that which 
entitles us to infer the one from the other — is the Con- 
sequence. The essence of the Syllogism, and all that is 



THE ARISTOTELIG ANALYSIS. 177 

actually affirmed in it, is this necessary consequence of the 
Conclusion fi'om the Premises. Hence the Syllogism is 
really one, — a single and indivisible act of Thought. 
Though apparently complex — though, in a certain sense, 
including three Judgments — it does not affirm either one 
of them taken separately, but only the necessary depend- 
ence of one upon the two others. Thus, as we have seen, 
both Premises may be false, and the Conclusion may be 
false ; and yet the Syllogism may be valid or correct in 
Form, for the latter may be legitimately deduced from the 
former. The following, for example, is a vahd inference, 
though each of the Propositions is false. 

All men are immortal , 

All bipeds are men ; 

Therefore^ all bipeds are immortal. 
Hence, in order to dispute or deny a Syllogism as such, we 
do not need to deny either of its three Judgments, but 
only the Consequence, or the dependence of the Conclu- 
sion upon the Premises ; in other words, a single negation 
denies all that the Syllogism, which is but one act of 
Thought, asserts. We say, it does not follow that A is B 
BECAUSE A is some M and B is some M ; though possibly 
A is B for some other reason. 

In explanation of the terms employed to denote the pro- 
cess of reasoning, the following passage is borrowed from 
Su- Wilham Hamilton's Lectures on Logic : " Beasoning 
is a modification fi-om the French raisonner (and this is a 
derivation from the Latin ratio') and corresponds to ratio- 
cinatio, which has, indeed, been immediately transferred 
into our language under the form ratiocination. Ratiocina- 
tion denotes properly the process, but improperly also the 
product, of reasoning ; ratiocinium marks exclusively the 
product. The original meaning of ratio was computation, 
and fi'om the calculation of numbers it was ti-ansferred to 
the process of mechate comparison in general. Discourse 

8* I. 



178 MEDIATE INFERENCE OR SYLLOGISM. 

(discursm, Bidvoia) indicates tlie operation of comparison, 
the running backwards and forwards between the char- 
acters or notes of objects ; this term may therefore be 
properly appUed to the Elaborative Faculty in general 
[the Understanding]. The terms discourse and discursus 
are, however, often, nay generally, used for the reasoning 
process strictly considered, and discursive is even applied 
to denote Mediate, ia opposition to Intuitive [or Imme- 
diate], judgment, as is done by Milton. 

* Whence the soul 
Reason receives, and reason is her being, 
Discursiye or intuitive ; discourse 
Is oftest yours.' 

The compound term, discourse of reason, unambiguously 

marks its employment in this sense. 

'A beast that wants discourse of reason 
Would have mourned longer.' 

Argumentation is derived from ojrgumentari, which means 
argumentis uti. Argument again Qargumentum') — what 
is assumed in order to argue something — is properly the 
middle notion in a reasoning, — that through which the 
Conclusion is estabhshed. It is often, however, applied 
as coextensive with argumentation. Inference or illation 
(from itifero') indicates the carrying out into the last Prop- 
osition what was virtually contained in the antecedent 
Judgments. To conclude (concludere'), again, signifies the 
act of connecting and shutting into the last Proposition the 
two notions which stood apart in the two first. A conclu- 
sion is usually taken, in its strict and proper signification, 
to mean the last Proposition of a reasoning ; it is some- 
times, however, used to express the product of the whole 
process. To syllogize means to form Syllogisms. Syllogism 
(<Tv\\oyiafjL6<i^ seems originally, like ratio, to have denoted 
a computation, — an adding up, — and, Hke the greater part 
of the technical terms in Logic in general, was borrowed 



THE ARISTOTELIC ANALYSIS. 179 

by Aristotle from the mathematicians. This primary- 
meaning of these two words favors the theory of those 
pliilosophers who, like Hobbes and Leidenfrost, maintain 
that all Thought is, in fact, at bottom, only a calculation, 
a reckoning. ^vXKojiafi6<; may, however, be considered 
as expressing only what the composition of the word de- 
notes, — a collecting together ; for a-vWojc^eadat comes 
from (TvXkeyecv-, which signifies to collect. Finally, in 
Latin, a Syllogism is called collectio, and to reason, colligere. 
This refers to the act of collecting, in the Conclusion, the 
two notions scattered in the Premises." 

Thus the unifying office of the Understanding, to which 
we have before adverted, is again brought to view. As a 
Judgment is an act whereby the two notions which are its 
Terms are brought together into one, so a Syllogism — 
Reasoning proper — Mediate Inference — is that act of 
Pure Thought whereby the two Judgments Avliich are its 
Premises are collected and summed up into one in the 
Conclusion ; or, what is the same thing expressed in relation 
to the Terms, whereby three notions are reduced to unity. 

" Without the power of Reasoning," says Hamilton, 
"we should have been limited in our knowledge (if 
knowledge under such a limitation would deserve the 
name of knowledge at all) — I say, without Reasoning, 
we should have been limited to a knowledge of what is 
given by Immediate Intuition ; we should have been 
unable to draw any inference from this knowledge, and 
have been shut out from the discovery of that countless 
multitude of truths, which, though of high, of paramount 
importance, are not self-evident. This faculty is hkewise 
of pecuhar utility, in order to protect us in our cogitations 
from error and falsehood, and to remove these, if they 
have already crept in. For every, even the most com- 
plex, web of thought may be reduced to simple Syllo- 
gisms ; and when this is done, their truth or falsehood, at 



180 MEDIATE INFERENCE OR SYLLOGISM. 

least in a logical relation, flashes into view." Hence, as 
Dr. Whately remarks, "the Syllogistic theory does not 
profess to furnish a peculiar method of reasoning, but only 
to set forth a method of analyzing that mental process wliich 
must invariably take place in all coiTCct reasoning " ; and 
again, •"' a Syllogism is evidently not a peculiar kind of 
argument, but only a peculiar form of expression in which 
every argument may be stated." 

The power of reasoning, of drawing Mediate Inferences, 
like that of framing Concepts, is at once a proof of man's 
superiority over the brutes, and of his inferiority to his 
Creator. Brutes cannot reason, nor even form Judgments 
respecting classes of things, their knowledge being con- 
fined, as we have seen, to Intuitions, — to Singulars. On 
the other hand, the Infinite Mind knows immediately or 
intuitively the relation of one thing or class of things to an- 
other, without being compelled to ascertain indirectly their 
agreement or non-agreement through their relations to a 
thu'd or Middle Term. The power of Mediate Inference is 
a help for an imperfect intellect ; Omniscience needs no help. 

The brief view which has now been given comprises all 
the essential principles of Mediate Inference, — that is, all 
the rules to which all Syllogisms, whatever may be their 
peculiarities in other respects, must conform. They may 
be summed up as follows : — 

1. A Syllogism must contain three Terms, and no more ; 
namely, the two whose agreement or disagi'eement we wish 
to ascertain, and the Third or Middle, with which each of 
these is separately compai'ed. If there were four Terms, 
two of them must be intermediate, not appearing in the Con- 
clusion ; but then the Premises Avould have no common Term. 
If we know only that A is 31 and B is iV, we have no 
means of ascertaining the relation of -4 and B to each other. 

2. A Syllogism must contain three Judgments, and no 
more ; namely, the two in which each of the Terms of the 



THE ARISTOTELIC ANALYSIS. 181 

Conclusion is compared with the Middle Term, and that in 
which these two are compared with each other. 

3. The Middle Term must he distributed (taken univer- 
sally^ in at least one of the Premises. The necessity of 
tliis Rule arises, as we have seen, from the fact that the 
two Extremes, in order to be compared with each other, 
must have been separately compared Avith the same com- 
mon 3Iiddle. If we consider no other kinds of Quantity 
than all and some (Universal and Particular), the Rule as 
here expressed is sufficient. But if we take into more 
definite view the Quantity of some, — namely, whether it 
does or does not exceed 07ie half, — the Rule may be made 
seemingly less stringent. It is enough that the quantifica- 
tions of the Middle Term in both Premises, added together, 
should exceed unity, — that is, exceed its possible totality 
or its distribution in any one ; for the amount of such 
excess over unity then constitutes a common Middle Term. 
Something mo7-e than all the Middle Term has been men- 
tioned in the Premises ; and both Terms in the Conclusion 
must have this excess as a common element. If A is three 
fourths of 31, and B is one half of 31, then at least 07ie 
fourth of M IS common to A and B ; and their agreement 
Avith this common temi is enough to insure their agreement 
with each other. This is called by Hamilton the ultra-total 
quantification of the Middle Term. It deserves mention, but 
as it is of very infit'equent use, the Rule as first enounced 
for the quantification of the Middle is practically sufficient. 

4. One Premise at least must he affirmative ; for if both 
Pi'emises are negative, the Middle Term agrees with 
neither of the two others, and therefore affords no ground 
for any Inference as to their agi'eement or non-agreement 
with each other. Though we know that A is not 3/ and 
B is not 31, we do not thereby know whether A is or is not 
B. A good general is not a coward, and Pompey was not 
a coward ; but these two assertions furnish no reason for be- 
heving that Ponipoy either was, or was not, a good general. 



182 MEDIATE INFEEENCE OR SYLLOGISM. 

5. If either Premise is negative^ the Conclusion is nega- 
tive ; for as one Premise, according to the preceding Rule, 
must be affirmative, if the other Premise is negative, there 
is a difference in the relation of the two principal Terms to 
the Middle Term, and hence a non-agreement between the 
two Terms themselves. 

6. Neither Term must he distributed in the Conclusion if 
it was not distributed in the Premise; for if only some is 
premised, we cannot conclude all. 

Logicians have usually added two other Rules, that the 
Conclusion follows the weaker part, a Negative being re- 
garded as weaker than an Affirmative, and a Particular as 
weaker than a Universal ; and that no Conclusion can he 
drawn from two Particular Premises. But both of these 
result only from a combination of Rules .5 and 6 with 3 ; 
hence they hardly need to be considered here, but I ap- 
pend a demonstration of them in the note.* No syllogism 

* As the two additional Rules were constructed with special reference to 
the Aristotelic doctrine of Judgments, they can be conveniently demon- 
strated only by bearing in mind the following maxims, which have already 
been laid down in the exposition of tliat doctrine. 

1. By Subalternation, Particular Judgments are included under their 
corresponding Universals ; that is, if A is true, I is also true ; and the 
same holds good of E and O. 

2. The Subject of a Judgment, taken universally or particularly, is that 
which renders the Judgment itself Universal or Particular. 

3. The Predicate of an Affirmative Judgment is always considered as 
Particular. 

4. The Predicate of a Negative Judgment is always regarded as Univer- 
sal, — that is, as distributed. 

Now there must always be in the Premises one more Term distributed than in 
the Conclusion; for by Rule 3, the Middle Term (which does not appear in 
the Conclusion) must be distributed in at least one of the Premises ; and 
by Rule 6, if any Term is distril>uted which docs appear in the Conclu- 
sion, it must also be distributed in the Premises. Then it follows that no 
Conclusion can be draiim from two Particular Premises. For if these are I 
and I, as neither Subject nor Predicate of I is Universal, the Middle Term 
IS not distributed. If they are I and O, then, by Rule 5, the Conclusion is 



THE AKISTOTELIC ANALYSIS. 188 

can be invalid which does not violate one or more of the 
six Rules first enounced. 

After the usual manner of logicians, the foregoing Rules 
have been summed up in these mnemonic hexameters : — 

Distribuas medium, nee quartus terminus adsit; 
Utraque nee pramissa negans, nee particularis ; 
Sectetur partem conclusio deteriorem, 
Et non distribuat nisi cum praemissa, negetve. 

But the application of these rules may become a matter 
of considerable complexity, when it is considered that, from 
the same naked (unquantified) Terms, a great variety 
of different Syllogisms may be formed. Each of the three 
Terms may be either Particular or Universal ; each of the 
three Judgments, either Affirmative or Negative : the Judo;- 
ments may be placed in any order with respect to each 

negative ; then its Predicate is distributed ; and Rule 6, taken in conjunc- 
tion with what has just been stated respecting tlie number of distributed 
Terms in the Premises, requires one of these Premises to be Universal. 

Again, if eitlier Premise is Particular, the Conclusion must be Particvlar, 
For the Subject of a Universal Affirmative Conclusion must be Universal ; 
therefore, in the Premise wherein this Subject appears, it must, by Rule 6, 
be Universal, and the Middle Term, which is therein joined with it, must 
consequently he Particular, since it must be the Predicate of an Affirmative 
Judgment. Then the Middle Term, in order to be once distributed, must 
be the Universal Subject of the other Premise. Hence, if the Conclusion is 
Universal Affirmative, both Premises must be Universal. 

And if the Conclusion is Universal Negative, both Premises must also be 
Universal. For both Terms of the Conclusion arc then distributed ; and as 
the Middle Term must also be distriltutcd, there must be at least three 
Terms distributed in the Premises. But this cannot be, unless both Prem- 
ises are Universal, since both of them, by Rule 4, cannot be Negative. 
Hence, whether the Conclusion is Affirmative or Negative, if it be Univer- 
sal, both Premises must be Universal. Then, if either Premise is Particular, 
the Conclusion must be Particular. 

But according to Rule 5, if either Premise is Negative, the Conclusion 
is Negative. Then, the Conclusion must follow the weaker part ; — that is, it 
must be Particular, if either Premise is Particular, and Negative, if either 
Premise is Negative. — Q. E. D. 



184 MEDIATE INFERENCE OR SYLLOGISM. 

other, and for three Judgments, six different orders of posi- 
tion are possible ; and each of the three Terms may be 
either Subject or Predicate in either or both of the Prem- 
ises, the two principal Terms also assuming either place in 
the Conclusion. The larger portion of the numerous Syl- 
logisms thus formed, it is true, are invalid, as offending 
against one or more of the preceding Rules. We need 
some more succinct mode than that of severally applying 
to each Syllogism all these Rules, before we can be satisfied 
that it is impeccable. Many of these Syllogistic forais, 
moreover, are equivalents of each other ; that is, the Rea- 
soning may be changed from one form to another, with- 
out impairing its validity, or even changing its signification 
in any essential respect. But of these equivalent forms 
some are more natural and obvious than the others ; the 
mind seeks for these by preference ; and when the process 
of reasoning appears in one of these natural and preferred 
forms, its validity is determined with ease and in a mo- 
ment. The application of the Rules to such cases is made 
Avith the quickness of instinct, and may be reduced almost 
to a mechanical process. 

A highly ingenious, though artificial, system has been 
contrived of classifying these numerous Syllogistic forms 
under a few heads, throwing out at once all that are ille- 
gitimate, immediately recognizing the remainder, and then 
transmuting those which are valid in substance, but un- 
natural and obscure in form, into the easy and familiar 
types in which the mind quickly perceives their legitimacy. 
Tlie study of this system, a ready use of Avhich may be 
said to constitute the art of Syllogizing, is facilitated by a 
series of mnemonic contrivances, many of them of mar- 
vellous ingenuity and completeness. The notation and 
most of the operations are of an algebraic character ; and 
attempts have not been wanting of late years to enlarge 
and perfect the system by a further introduction of mathe- 



THE ARISTOTELIC ANALYSIS. 185 

matical signs and processes. The failure of such an under- 
taking is not to be wondered at, for it px'oceeds, as it seems 
to me, upon a mistaken opinion as to the relative position 
of the two sciences. Logic is not a department of mathe- 
matics. Rather the reverse is true. Mathematics is the 
science of pure quantity^ — of reasoning about dimensions 
and numbers in the abstract, or as mimodified by any of 
tlie differences of quality by which all the objects of thought 
are actually distinguished ; and it is, therefore, only a de- 
partment, or a special application, of the far more compre- 
hensive science which has for its object Reasoning itself 
and all its subsidiary processes, and thus covers the whole 
domain of Pure Thought. All computation is reasoning ; 
but all reasoning is not computation, and therefore cannot 
be carried on by the processes, or be made subject to the 
special laws, of pure mathematics. 

Syllogistic forms are classified with respect to Mood and 
Figure, the former having regard to the value of the three 
component Judgments, and the latter to the relative j'WSi- 
tion of the three Terms in these Judgments. It will be 
convenient, then, to have a uniform mode of designating 
these three Terms. In future, S will stand for the Sub- 
ject, and P for the Predicate, of the Conclusion, and J/for 
the Middle Term. The Consequence, or what we usually 
express by the words therefore, consequently, &c., will be 
indicated by three dots placed thus .•. For example : — 

Mis P; 
S is M; 
.-. S is P. 

To facilitate reference, the Logicians have given special 
names to these several Terms and Judgments. The 
Predicate of the Conclusion is called the Major Term, and 
its Subject the 3Iinor Term. The Premise in which the 
Major is compared with the Middle Term is called the 
Major Premise^ and that in which the Minor is compared 



186 MEDIATE INFERENCE OK SYLLOGISM 

with the Middle, is the Minor Premise. These names 
have reference to the Quantity of Extension only, and are 
founded upon the received doctrine, that the natural order 
of predication is that in which the Genus is predicated of the 
Species, the Species of the Individual, and, generally, the 
Extensive whole of its part. Then the more Extensive 
Term, the Major, usually occupies, at least in Affirmative 
Judgments, the Predicate's place. " This," says Dr. 
Thomson, " is the natural, though not invariable, order ; 
and it is worthy of remark, that, even in Negative Judg- 
ments, where, from the negation, the two Terms cannot be 
set together to determine their respective Extension, if, 
apart from the Judgment, we know that the one is a small 
and the other a large class, — the one a clearly determined 
and the other a vague notion, — we naturally take the 
small and clearly determined Concept for the Subject. 
Thus, it is more natural to say that the. Apostles are not 
deceivers^ than that No deceivers are Apostles. So that, if 
our minds are not influenced by some previous thought to 
give greater prominence to the wider notion, and so make 
it the Subject," thus reversing the primary and natural 
order, the Term of major Extension will always be the 
Predicate, and that of minor Extension, the Subject. 

As these names — Major, Middle, and Minor — thus 
correctly indicate the comparative Extension of the three 
Terms, an Affirmative Syllogism in which these Terms 
occupy their natural place is conveniently symbolized by 
three concentric circles, of which the outermost and largest 
indicates the Predicate of the Conclusion, or the Major 
Term ; the innermost and smallest, the Subject of the Con- 
clusion, or the Minor ; and the intermediate one, the 
Middle Term. Thus : — 

All mammals arc viviparous ; All M are P. 

All whales are mammals ; All S are M. 

.•, All whales arc vivii^arous. .-. All S are P. 




THE ARISTOTELIC ANALYSIS. 187 

Here the reasoning is, that <S, which is a part of M^ 
must also be a part of -P, since 3/ is a part of jP. We are 
thus led to another mode of enunciating the governing 
principle of all Syllogisms, that a part of a part is a part 
of the whole ; or, as Leibnitz expresses it, contentum contenti 
est contentum continentis. Tliis principle agrees in every 
essential respect with the famous Dictum of Aristotle, 
usually called the Dictum de omni et nulla, that whatever is 
jjredicated (affirmed or denied) universalis/ of any Class 
(i. e. of any whole), may be also predicated of any part of that 
Class. Both principles have been already recognized and 
a})plied in the doctrine of Subalternation. The name of 
this Dictum is derived from the two forms which it assumes 
as applied either to affirmative or negative Conclusions ; 
the Dictum de omni being thus expressed, Quicquid de 
omni valet, valet etiam de quibusdam et singulis ; and the 
Dictum de nullo being, Quicquid de nullo valet, nee de qui- 
busdam nee de singidis valet. Both of these principles are 
evidently of a secondary or derivative character, their af- 
firmative and negative forms being grounded respectively 
upon the two Axioms of Identity and Non-Contradiction ; 
for as a whole is identical with the sum of all its parts, 
whatever is affinned or denied (distributively) of the 
whole is thereby affirmed or denied of each of its parts. 
Burgersdyck remarks, that, for the purpose of applying the 
Dictum to Syllogisms, it may more conveniently be thus 
expressed : Whatever Predicate is universally affirmed or 
denied of any 3Iiddle Term or Part is also affirmed or de- 
nied of any Subject which is contained under that inter- 
mediate Term or Part. 

The mode of symbolizing the mutual relations of the 
three Terms of a Syllogism, which is applied above to a 
Universal Affirmative, may be extended to Negatives and 
Particulars. The total disagreement of two Terms with 
each other, which is expressed by a Negative Judgment, is 



188 



MEDIATE INFERENCE OR SYLLOGISM. 





properly indicated by two Circles which do not coincide in 
any part. Thus : — 



No M is P ; 
All S is M ; 
No S is P. 



Both the partial agreement, and the partial disagreement, 
of two Terms, — as these are merely two aspects of one 

and the same Thought, — 
are properly indicated by 
the same symbol, namely, 
two circles which intersect. 
Some S are M, and tSome 
S are not M^ are both ex- 
pressed by this symbol. 
Excepting this ambiguity, 
all Syllogisms can be adequately symbolized by some com- 
bination of the preceding diagrams. 

Hitherto we have regarded the Syllogism only as a 
means of evincing; the relation of two Terms to each other 
through the relation of each to a common or Third Term. 
But the Dictum as expressed by Burgersdyck indicates 
another aspect of the Syllogism, equivalent indeed to the 
former one, but m certain respects more convenient for 
use. The Judgment in which " a Predicate is universally 
affirmed or denied of any Middle Term or Part " is a G-en- 
eral Rule; the Judgment that a given '"Subject is con- 
tained under that intermediate Term or part," is the Suh- 
sumption of this Subject under the condition of that Rule ; 
and then the Conclusion folloAving, that the given Subject is 
governed by that Rule, is a solution of the doubt with which 
wc commenced, whether S is, or is not, P. Every Syllogism, 




THE ARISTOTELIC ANALYSIS, 189 

then, must consist of three Judgments, one of which must 
be a General Rule, or, as Hamilton expresses it, a Sump- 
tion ; another must be the Subsumption of a certain Sub- 
ject under that Rule ; and the third is the Conclusion^ 
that this Subject is determined by the Rule. Thus : — 

Sumption. No one who is content is miserable ; 

Subsumption. Some of the poor are content ; 

Conclusion. Some of the poor are not miserable. 

It is not difficult to prove, say the Port Royal logicians, 
that all the Rules which we have given serve only to show 
that the Conclusion is contained under (or embraced in the 
Extension of) one of the Premises, which is a General 
Rule or Sumption, and that the other Premise, the Sub- 
sumption, shows this ; and that arguments are vicious only 
when they fail to observe this method, and are always good 
when it is observed. 

Kant expresses tlie general law of the Syllogism, as thus 
conceived, in the following formula : Whatever stands 
under the condition of a Mule, that stands also under the 
Mule itself. As the former view regards chiefly the three 
Terms, so this one has primary reference to the three 
Judgments, of which every Syllogism is composed. The 
former view does not contradict the latter ; they are only 
two aspects of the same thing. But what we have hitherto 
termed the Major Premise, though it is usually the same 
Judgment that is here called the Sumptiori, is not always 
so. Thus, in the following Syllogism, (called by the 
Logicians Disamis of the Third Figure,) the first Judg- 
ment, as it contains the Predicate of the Conclusion, is the 
Major Premise ; but the second Judgment is the Sumption. 
Some wicked persons are men of high rank ; 
All the wicked are miserable. 
.'. Some miserable persons are men of high rank. 

As it has been demonstrated that/rom two Particulars no 
Conclusion can be drawn, every Syllogism must have for a 



190 



MEDIATE INFERENCE OR SYLLOGISM. 



Premise at least one Universal Judgment ; that is, one of 
its Premises must be a Sumption or General Rule. In the 
First Figure, which is the only natural and obvious form 
of reasoning, and to which all the other forms can be re- 
duced, the Sumption is always the Major Premise. 



1. Figure and Mood. 

The Figure of a Syllogism depends upon the relati- 
position of its three Terms, and is determined by the po 
tion of the Middle Term in the Premises. Now the M' 
die Term may be either the Subject of the Major Premise, 
and the Predicate of the Minor, in which case we say the 
Syllogism is of the First Figure ; or it may be the Predi- 
cate of both, which is the Second Figure ; or it may be the 
Subject of both, thus constituting the Third Figure ; or it 
may be the Predicate of the Major and the Subject of the 
Minor, thus converting the First, and giving rise to the 
Fourth Figure. Accordingly, the four Figures are thus 
indicated. 



I 



I. 


II. 


III. 


IV. 


MP 


PM 


MP 


PM 


SM 


SM 


MS 


MS 


SP 


.-. SP 


.-. SP 


.-. SP 



They are also indicated in the following mnemonic 
line : — 

Siib prce ; turn prce proe. ; turn sub sub ; turn prce sub. 

The line should be read thus : — The Middle Term is, first, 
SutiJQct, Predicate ; then, Predicate, Predicate ; then, Sv^- 
ject. Subject ; lastly. Predicate, Subject. 

The Fourth Figure is not recognized by Aristotle, but is 
accepted, if at all, on the supposed authority of Galen. 
Most modem logicians reject it, not as invahd, but as un- 
natural and unnecessary. As we have already said, the 



nCURE AND MOOD. 191 

natural order of predication is that in which the Genus is 
predicated of the Species, or tlie more Extensive of the less 
Extensive Term. Then it follows that the First is the 
only natural and obvious Figure, as it is the only one 
which observes this order throughout. Here, the Predicate 
of the Conclusion, which is the Term of widest Extension, 
appears as the Prechcate of the Major Premise ; and the 
Subject of the Conclusion, being the Term of least Exten- 
sion, is the Subject of the Minor Premise, — the Middle 
Term appearing, as it ought, intermediate between the 
two, being of less Extension than P, and greater than S. 
Here also, as Dr. Thomson remarks, the Conclusion in no 
way disturbs the order of Terms which was first established 
in the Premises ; for the Subject of the Conclusion appears 
also as a Subject in the Premises, and the Predicate as a 
Predicate ; — that is, no Thought which was primary be- 
comes secondary, nor any secondary primary. Take, for 
instance, the following Svlloo-ism in the First Figure : — 

1. No boaster deserves respect ; 
Some heroes are (some) boasters ; 

.'. Some heroes do not deserve respect. 

Here, everything is in its natural place ; each Subject is of 
less Extension than its Predicate, and the Terms preserve 
the same relative places in the Conclusion which they 
occupied in the Premises. 

But change this Syllogism into the Second Figure, by 
converting the Major Premise, thus : — 

2. No person deserving respect is a boaster ; 
Some heroes are (some) boasters ; 

.*. Some heroes do not deserve respect. 

Here, the natural order is violated in one half of the rea- 
soning ; for the Subject of the Major is the Predicate of 
the Conclusion, and has wider Extension than its own 
Predicate. 



192 MEDIATE INFERENCE OR SYLLOGISM. 

Again, change the same Syllogism into the Third Fig- 
ure, by converting the Minor Premise, thus : — 

3. No boaster deserves respect ; 
Some boasters are (some) heroes ; 

.'. Some heroes do not deserve respect. 
Here, the other half of the reasoning appears unnatural 
and forced. The Predicate of the Minor Premise becomes 
the Subject of the Conclusion, and is of less Extension 
than its own Subject. 

To change this Syllogism into the Fourth Figure, we 
must convert both Premises, thus : — 

4. No person deserving respect is a boaster ; 
Some boasters are (some) heroes ; 

.'. Some heroes do not deserve respect. 
HereVboth halves of the reasoning are contorted, so that it 
appears wholly unnatural. Not only is the Predicate of 
the Minor the Subject of the Conclusion and of less Extent 
than its own Subject, but the Subject of the Major is the 
Predicate of the Conclusion, and of greater Extent than its 
own Predicate. The mind revolts at this perversion ; 
striving to preserve the same order in the Conclusion 
which it observed in the Premises, the Conclusion which it 
would naturally draw from these two Premises is this : — 

No person deserving respect is (some) hero. . 
Now, this Conclusion, which is natural and obvious, is the 
Converse of the former one, which was unnatural ; and it 
reduces the Syllogism (changing the order of the Premises) 
from the Fourth to the First Figure. Hence it appears, 
that what is called the Fourth Figure is only the First 
with a converted Conckision ; that is, we do not actually 
reason in the Fourth, but only in the First, and then, if 
occasion requires, convert the Conclusion of the First. 
Tlie reasoning is indirect, or Mediate in a double sense ; 
the nominal Conclusion of the Fourth is actually, but in- 



FIGURE AND MOOD. 193 

directly, obtained by converting the Conclusion of the 
First. Hence, many Logicians exchide the Fourth alto- 
gether, and call those Syllogistic forms which would other- 
wise fall under it " indirect Moods of the First Figure." 
But we can also obtain, if we see fit, indirect Moods from 
the Second or Third Figure, by convertmg their Conclu- 
sions also. There is no reason, then, for giving a special 
class of these " hidirect Moods " to the First Figure, any 
more than to the Second or Third ; that is, there is no 
reason for considering the Moods of the so-called Fourth 
Figure at all. It is not only unnatural, but wholly un- 
necessary. We need only state, that, after obtaining the 
ordinary mediate Conclusions from either of the three Fig- 
ures, we may, if occasion requires, obtain a second set of 
Conclusions immediately, by converting the former ones. 

But we observe, secondly, that the natural but unex- 
pressed Conclusion of the so-called Fourth, — 

" No person deserving respect is (some) hero," — 
is a shockino[ one for the Aristotelians, foi* it is a Negative 
with an undistributed Predicate. They will not allow that 
such a Judgment is possible ; but here it appears as actual, 
— nay, as the only natural result of Premises to which, 
according to the Aristotelic doctrine, only a wholly unnat- 
vral Conclusion can be given by inventing a so-called 
Fourth Figure, otherwise not needed, and in every respect 
jierverted and contrary to nature. Of course, Sir William 
Hamilton, whose system expressly recognizes these Nega- 
tive Judgments (Ani) with undistributed Predicates, has 
taken advantage of this fact, and pressed it as an unanswer- 
able argument against his opponents. 

But to return to the Aristotelic doctrine. The reason 
ordinarily given for awarding a decided preference to the 
First over the other Fioui-es is not either of the two here 
alleged, but one which inunediately results I'rom them, — 
namely, that the Dictum de omni et 'rmllo, which is held to 



194 



MEDIATE INFERENCE OR SYLLOGISM. 



be a universal principle of all reasoning, is directly appli- 
cable only to the First Figure. This Dictum, which has 
respect exclusively to the Quantity of Extension, neces- 
sarily supposes that the order of Extension is strictly fol- 
lowed in the Syllogism ; that is, that the Predicate in each 
of its three Judgments should be of wider Extension than 
the Subject. This is the case in the First Figure ; but as 
we have seen, it is not so with the others. In the Second, 
the Subject of the Major, and in the Third, the Subject of 
the Minor Premise, has a wider Extension than the corre- 
sponding Predicate. In order to show that the Dictum is 
universally applicable, we must be able to reduce all Syllo- 
gisms, in wliatever class they may at first be ranked, to the 
First Figure. Now, to judge from the instance just given, 
in which we have carried the same Syllogism successively 
through each of the four Figures, such a Reduction can be 
very easily accomplished. It is only necessary to convert 
one or both of the Premises. Recurring for a moment to 
tiie first mode of indicating the variations of Figure, — 



I. 


II. 


III. 


IV. 


MP 


PM 


MP 


PM 


SM 


S M 


MS 


MS 


SP 


.-. SP 


.-. SP 


.-. SP 



it is easy to see that the Second Figure is reduced to the 
First by converting its Major Premise ; the Third, by con- 
verting its Minor; and the Fourth, by converting both. 
But as the order of the Premises may be transposed, as the 
Sumption and the Major Premise do not always coincide, 
and as the Judgment O, on the strict Aristotelic doctrine, 
is not convertible at all, it is not always easy to tell which 
Premise ought to be converted, and the . pi'ocess of Re- 
duction practically becomes so complex and. intricate, that, 
to facilitate it, an elaborate system and a whole set of 
mnemonics have been contrived. These will be explained 
hereafter. 



FIGURE AND MOOD. 195 

The Ai'istotelic logicians appear to hesitate, or be in 
doubt, as to the motives for reducing the three lower Fig- 
ures to the First. At times, they speak as if the only 
reason for such Reduction were tlie one already mentioned, 
— to reduce all Syllogistic forms to system by showing that 
they are all controlled by one governing principle, the Dic- 
tum de omni et nidlo. The implication then is, that they 
are valid or competent forms of reasoning, even before such 
Reduction ; and that they are reduced, therefore, only to 
render them more systematic and orderly in appearance. 
Then, again, they speak o^ proving them by this Reduction, 
as if otherwise they were weak and needed proof, even if 
they were not invalid. The truth is, the reasoning under 
either of these Figures is just as conclusive as under the 
First. In neither case can the Conclusion be denied with- 
out involving the denier in an absurdity, — that is, in a con- 
tradiction of one of the Primary Axioms of Pure Thought. 
Nay, more ; in certain cases, it is, in one sense, more 
natural to make inferences by the Second or Third Figure, 
than by the First ; that is, the particular object which we 
have in view in the general investigation or course of argu- 
ment which we are pursuing, may more directly lead us to 
the former than to the latter. Thus, Avlien we wish to 
exclude somethino; from a class to which it had been 
wrongly assigned, or to disprove something which has been 
asserted, we are most frequently led to argue in the Second 
Figure, since any Conclusion in this Figure must be nega- 
tive ; for as the Middle Term is here Predicate in both 
Premises, it cannot be distributed unless one of the Prem- 
ises is negative, and then, by Rule 5, the Conclusion is 
negative. " The arguments," says Whately, " used in the 
process called Abscissio infiniti, will, in general, be the most 
easily referred to this Figure. This phrase was applied by 
some logiciauh, to a series of arguments used in any inquiry 
in wliich we go on excluding, one by one, certain suppo 



196 MEDIATE INFERENCE OR SYLLOGISM. 

sitlons, or certain classes of things, from that whose real 
nature we are seeking to ascei'tain." 

Again, if our design is to establish exceptions to a pre- 
tended law or rule, — that is, if we would disprove the as- 
serted universality of the Proposition, — the Third Figure 
will most commonly answer our purpose, for here all Con- 
clusions must be Particular; we prove that Some are^ or 
Some are not, and thus disprove the assertion that All are 
not, or All are. Conclusions in the Third Figure must be 
Particular, because both Teims of the Conclusion aj^pear 
as Predicates ui the two Premises ; hence, if these Prem- 
ises are both Affirmatives, their Predicates are Particular ; 
and if one of them is Negative, the Conclusion can only be 
a Particular Negative, since a Universal Negative distrib- 
utes both its Terms. 

Because the two lower Figures are thus not only valid 
in themselves, but peculiarly appropriate for certain pur- 
poses, some logicians hold that it is unnecessary to reduce 
them to the First Figure. Each of the three, they main- 
tain, has its own functions and its own governing principle. 
The principle wdiich is assigned to the First, needs but to 
be slightly modified in order to be directly applicable to 
the Second or the Third ; since all three are but various 
applications of the same Axioms of Thought. Thus, if the 
Dictum de omni et nullo be considered as the principle for 
the First Figure, for the Second we have the Dictum de 
diverso, — that if one Term is contained in, and another ex- 
cluded from, a third Term, then they are excluded from each 
other. For the Third Figure, the principle is called the 
Dictum de exejnplo, — that two Terms which contain a com- 
mon part partly agree ; or, if one cotitains a part which the 
other does not, they partly differ. 

Reduction is not essential, therefore, but it is certainly 
convenient ; the reasoning does not become more cogent by 
being reduced to the First Figure, but it is rendered more 



FIGURE AND MOOD. 197 

perspicuous, more simple and natural in expression, and 
any fallacies in it, which might otherwise escape notice, 
become at once so obvious that they cannot avoid detection. 
The whole theory of argumentation, moreover,, is rendered 
more systematic and elegant, when its numerous modes 
are reduced to a very few fundamental fonns, the validity 
of which is so manifest that they do not need to be tested 
by the application of previously determined rules. 

The proper relative position of the three Judgments of 
a Syllogism appears so obvious, on the Aristotelic doctrine, 
that it has usually been taken for granted. If we reason 
only in order to instruct, to convince, or to refute, — and 
no other purpose seems to have been contemplated by the 
old logicians, — the natural order of Thought seems to be, 
that the Ground or Reason should precede the Conse- 
quence ; that is, that the Premises, as their name imports, 
should precede, and, as it were, effectuate the Conclusion - 
And as regards the two Premises, if the reasoning is ex- 
clusively in the Quantity of Extension, the Major should 
be placed before the Minor, the Sumption or General Rule 
before the Subsumption. 

The Mood of a Syllogism is the value of its three Judg- 
ments considered in respect to their Quantity and Quality. 
Since there are but four kinds of Judgments as thus viewed, 
indicated respectively by the four vowels A, E, I, and O, 
it is evident that three of these letters must express any 
possible Mood. When Ave have ascertained its Mood and 
Figure, the classified place and formal value of a Syllogism 
are determined. For instance, E I O, Fig. I., and A A I, 
Fig. III., are thus expressed : — 



Fig. I. 




Fig. hi. 




No M is P ; 


E 


All M are P ; 


A 


Some S are M ; 


I 


All M are S ; 


A 


•• Some S are not P. 


O 


.*. Some S are P. 


I 



198 MEDIATE INFERENCE OR SYLLOGISM. 

As only four Judgments are possible, and three are 
necessary to constitute a Syllogism, the whole number of 
Moods can be niunerically determined. Only sixty-four 
different arrangements can be made out of four letters 
taken three at a time ; hence, sixty-four Moods are con- 
ceivable. But the greater number of these are invalid, as 
contradicting one or more of the General Rules which 
govern, as we have seen, all forms of Mediate Inference. 
The elimination of these invalid forms can be more easily 
effected, if we first reduce the expression of a Mood to its 
simplest form. 

Strictly speaking, only the two letters which denote the 
Premises need to be taken into account ; for the Quantity 
and Quality (and therefore the letter) of the Conclusion 
are determined by those of the Premises. Each Mood, 
then, being designated by only two letters, and only six- 
teen different arrangements being possible of four letters 
taken two at a time, all conceivable Moods are contained 



in the following 


Hst : — 






1.) A A 




2.) E A 


8.) I A 


4.) OA 


AE 




EE 


IE 


OE 


AI 




EI 


II 


OI 


AO 




EO 


lO 


OO 



The Rule that from two Negative Premises no Conclusion 
can he drawn, excludes four from this list, namely, E E, 
E O, O E, and O O. The Rule that no Conclusion can he 
drawn from two Particular Premises, excludes three more, 
namely, 1 1, I O, and O I. Finally, I E is excluded be- 
cause its Negative Conclusion distributes the Major Term, 
which is undistributed in I, the Major Premise ; but 
according to Rule 6, neither Term can he distrihuted in the 
Conclusion, if it was not distrihuted in the Premise. We 
may here observe, that the violation of this last Rule, in 
respect to the Major Tenn, is called illicit process of the 



FIGURE AND MOOD. 199 

Major ; in respect to the Minor Term, it is called illieit 
process of the Minor. 

These exclusions being effected, there remain but eight 
vahd Moods, namely, A A, A E, A I, A O, E A, E I, 
I A, and O A. Not all, even of these eight, however, 
afford a valid Syllogism in each of the four Figures ; for 
the altered position of the Middle Term may cause the 
greater number of them to offend against the Rules which 
forbid both an undistiibuted Middle and an Illicit Process 
whether of the Major or Minor Term. Special Rules 
have been enounced for each of the Figures, which will 
enable us to make the further exclusions that are requisite. 
It should be observed, that these Special Rules contain no 
new principle, but are immediately deducible ft'om the 
General Rules, that have already been established for all 
Syllogisms ; taking these General Rules in connection, how- 
ever, with the two axioms by which the Aristotelians de- 
termine the implicit Quantity of the P;-edicate ; namely, 
that, in all Affirmative Judgments, the Predicate is Par- 
ticular, and that, in all Negative Judgments, the Predicate 
is Universal. This deduction may be left as an exercise 
for the learner. We will here consider the Special Rules 
under that theory which regards every Mediate Inference 
as proceeding from the Subsumption of a particular case 
under a General Rule or Sumption ; Httle more than an 
alteration of phraseology will be needed to adapt them to 
the theory in which we speak only of Major and Minor 
Premises. 

The Special Rules for the First Figure are, — 

1. The Sumption must be Universal ; 

2. The Subsumption must be Affirmative. 

These two Rules exclude I A, O A, A E, and A O. 
There remain A A, E A, A I, and E I, as the only valid 
Moods in this Figure ; and these are named Barbara^ Ge- 
larent, Darii, and Ferio. Observe that the three vowels 



200 MEDIATE INFERENCE OR SYLLOGISM. 

in each of these names denote the Mood of the Syllogism 
to which it is applied ; and the same is true of the technical 
names which will be given to the vahd Moods in the other 
Figures. 

The Special Rules for the Second Figure are, — 

1. The Sumption must be Universal ; 

2. One of the Premises must be Negative, and there- 

fore the Conclusion must be Negative. 

These Rules exclude I A, O A, A A, and A I ; the? 
there remain as valid in the Second Figure only the four 
Moods which have been named Cesare, Camestres, Festino 
and Baroko. 

The Special Rules for the Third Figure are, — 

1. The Subsumption must be Affirmative ; 

2. The Conclusion must be Particular. 

Throwing out A B and A O under these Rules, there 
remain for the Third Figure six Moods, named Darapti. 
Disamis, Datisi^ Felapton, Bohardo, and Ferison. 

The Special Rules for the Foiirth Figure are, — 

1. If the Sumption is Affirmative, the Subsumption 
must be Universal. 

2. If either Premise is Negative, the Sumption must be 
Universal. 

3. If the Subsumption is Affirmative, the Conclusion 
must be Particular. 

Rejecting A I, A O, and O A, as offending against 
these Rules, there remain only five Moods, called Bra- 
mantip, Camenes, Bimaris, Fesapo, and Fresison, as valid 
in the Fourth Figure. 

Taking the four Figures together, therefore, there are 
nineteen valid Moods ; but as fifteen of these can be re- 
duced to those of the First Figure, there are only four 
Moods which are at once vahd, natui'al, and perspicuous. 
Regarding the last vowel in the names of these four (^Bar- 
bara, Celarent, Barii, Ferio)^ we see that these are just 



FIGURE AND MOOD. 201 

sufficient to prove the four fundamental Judgments, A, jB, 
I, and O. 

If we exclude the Fourth Figure altogether, considering 
Bramantip^ Camenes, &c. as indirect Moods of the First, 
there are but fourteen direct Moods. On the other hand, 
since from every Syllogism with a Universal Conclusion 
we can obtain, by Subalternation, a Particular Conclusion 
also, there are five other indirect Moods, which are anony- 
mous, making twenty-four in all. Thus, A A in the First 
yields I, as well as A, for a Conclusion ; and fi'om E A in 
the Second, we may conclude not only E, but O. But 
these anonymous Moods, besides being indirect, are prac- 
tically useless ; since it is idle to infer some only, when the 
Premises warrant the inference of all. 

Rejecting the Fourth Figure and the indirect Moods, 
it will be seen, fi'om examining the last vowel in each of 
the names, that A is proved only in one Figure and one 
Mood ; E in two Figures and three Moods : I in two Fig- 
ures and four Moods ; and O in three Figui'es and six 
Moods. " For this reason," says Mr. Mansel, " A is de- 
clared by Aristotle to be the most difficult proposition to 
establish, and the easiest to overthrow ; O, the reverse. 
And, generally, Universals are most easily overthrown, 
Particulars more easily established." 

The names of all the valid Moods have been put to- 
gether into the following mnemonic hexameters, which 
deserve cai'eful study, not only as a complete artificial 
system for the Reduction of all the Moods of the suborcU- 
nate Figures to those of the First, (for which purpose the 
names were invented,) but as a hterary curiosity. They 
have been in use in the Schools, as an aid to the mem- 
ory, for over six centuries, their authorship being un- 
known. Mr. DeMorgan calls them " the magic words 
which are more full of meaning than any that ever were 
made." Sir William Hamilton says of them that " there 

9* 



202 MEDIATE INFERENCE OR SYLLOGISM 

are few human inventions which display a higher inge- 
nuity." 

Barbara, Celarent, Darii, Ferioqub prioris. 
Cesare, Camestres, Festino, Baroko secundse. 
Tertia Darapti, Disamis, Datisi, Felapton, 
Bokardo, Ferison habet. Quarta insuper addit 
Bramantip, Camenes, Dimakis, Fesapo, Fresison. 

If, rejecting the Fourth Figure, we consider its contents 
as indirect Moods of the First, instead of the first hue, the 
two following should be substituted : — 

Barbara, Celarent, Darii, Ferio, BARALip-ton, 
Celantes, Dabitis, Fapesmo, FRisESOM-orum, 

the final syllables in italics being only euphonic. 

As already mentioned, the three vowels in each of these 
names indicate the Quantity and Quality of the three Judg- 
ments which form the Syllogism. The consonants in the 
names belonging to the First Figure have no special mean- 
ing ; but of those in the other Figures, every consonant 
(except T and n, which are merely euphonic) indicates 
some step to be taken in the process of reducing the Mood 
to a Mood of the First Figure. 

The initial consonant, which is either B, C, D, or F, 
indicates that Mood of the First Figure (j^arbara, Cela- 
rent, i)arii, or ^erio) to which the Reduction brings us. 
Thus, Cesare and Camestres are reduced to Celarent; Fes- 
tino^ Felapton, &c., to Ferio. The other consonants show 
how the Reduction is made, m indicates that the Premises 
are to be transposed ; s and p, that the Judgment indicated 
by the vowel immediately preceding is to be converted, — 
s, that it is to be converted simply, while p signifies the 
conversion per accidens. 

K, which occurs in the names of only two Moods, Ba- 
roko and Bokardo, denotes that the Judgment indicated 
by the preceding vowel is to be left out, another sub- 
stituted for it, and the process to be then completed by 



FIGURE AND MOOD. 



203 



a Reduction iper impossibile, which will be explained here- 
after. 

A few examples will sufficiently illustrate the process. 
The name Disamis indicates the following Syllogism of 
the Third Figure, which is to be reduced to Darii of the 
First, by converting simply its Major Premise, transposing 
its Premises, and then converting its Conclusion. 



Disamis 
Some M are P ; 
All M are S ; 
Some S are P. 



reduced to 



DARn. 
All M are S ; 
Some P are M ; 
.•• Some P are S. 



Some wars are justifiable ; 
All wars are inexpedient ; 
Some inexpedient acts are 
justifiable. 



All wars are inexpedient ; 
Some justifiable acts are wars ; 
.'. Some justifiable acts are inex- 
pedient. 

Festino of the Second is reduced to Ferio of the First 
Figure, by converting simply its Major Premise. 
Festino reduced to Ferio. 



No P is M ; 

Some S are M ; 
.*. Some S are not P. 

No ruminant is solid-hoofed ; 

Some herbivora are solid- 
hoofed ; 
•. Some herbivora are not rumi- 
nant. 



No M is P ; 
Some S are M ; 
.*. Some S are not P. 

No solid-hoofed animal is 

ruminant ; 
Some herbivora are soHd- 

hoofed ; 
. Some herbivora are not 
ruminant. 



Fesapo of the Fourth is reduced to Ferio of the First 
Figure, by converting both its Premises, the Major simply, 
and the Minor per accidens. 

Fesapo reduced to Ferio. 

No P is M ; No M is P ; 

All M are S ; Some S are M ; 

••. Some S are not P. .*. Some S are not P. 



204 MEDIATE INFERENCE OR SYLLOGISM. 

No Hindoo is white ; No white is a Hindoo ; 

All whites are civilized ; Some civilized are whites ; 

.'. Some civilized are not Hindoos. .•. Some civilized are not 

Hindoos. 

Baroko and Bokardo have been stumbling-blocks to the 
logicians. In order to reduce either of them to the First 
Figure, the Premise which needs to be converted is O ; 
but according to the old doctrine, O is inconvertible. To 
overcome this difficulty, the logicians invented the awk- 
ward, roundabout, and operose process which they called 
deduction per Impossibile. Through a Syllogism in Bar^ 
bara, they proved, not directly that the Conclusion in 
BaroJco and Bokardo is true, but that its Contradictory is 
false ; now, according to the Axiom of Excluded Middle 
(that two Contradictories cannot both be false), this is an 
indirect method of proving that the Conclusion is true. 
The process is as follows. 

Of course, both Premises in every Syllogism are pre- 
sumed to be true ; then, any Conclusion which contradicts 
either one of them must be false. Now, k indicates, that, 
instead of the Premise signified by the vowel (O) imme- 
diately preceding, we are to substitute the Contradictory 
of the Conclusion ; and as this Conclusion is O, its Contra- 
dictory is A. But from the two Premises (A A) thus 
obtained, we have a Conclusion which contradicts the origi- 
nal Premise, O. Then the substituted Judgment in A 
(which is the Contradictory of the original Conclusion) 
must be false ; and therefore the original Conclusion itself 
is true. This is not exactly reducing the Syllogism to the 
First Figure, but it is indirectly proving, through the First 
Figure^ that the Conclusion of the Syllogism must be true, 
because its Contradictory is false. 

Baroko reduced to Barbara. 

AU P are M ; All P are M ; ^^^^^-^^^^ 

Some S are not M ; All S are P ; (Contradictory of former Con- 

*. Some S are not P. .-. AU S are M. (Contradicts former Minor 

Premise.) 



FIGURE AND MOOD. 



205 



BoKARDo reduced to Bakbara. 

Some M are not P ; All S are P ; (Contradictory of former 

All M are S ; All M are S ; Conclusion). 

.•. Some S are not P. .*. All M are P. (Contradicts former Major 

Premise.) 

As this Conclusion in Barbara cannot be tnie, its 
Premise, which is the Contradictory of the former Con- 
clusion, must be false ; then the original Conclusion itself 
is true. 

All this is awkward enough. Whately and othei's 
rightly remark, that these two difficult Syllogisms can be 
reduced in a much simpler and ' more elegant manner, 
through converting one of their Premises by Contrapo- 
sition. Thus, let Baroko be now called FaJcoro, and let 
Bokardo be named Dokamok (the substitution of these two 
names Avill not spoil the mnemonic hexameters) ; and let 
K indicate Conversion by Contraposition. 

Fakoro reduced to Ferio. 



All P are M ; 
Some S are not M ; 
.'. Some S are not P. 
All murders are intentional ; 

Some homicides are not inten- 
tional ; 
.•. Some homicides are not mur- 
ders. 



Dokamok 



reduced to 



Some M are not P ; 
All M are S ; 
.*. Some S are not P. 

by Contraposition,) 
Some imprudent acts are 

not vicious ; 
All imprudent acts are foolish ; 



No not-M is P ; 
Some S are not-M ; 
.*. Some S are not P. 

No unintentional act is a 

murder ; 
Some homicides are unin- 
tentional ; 
.". Some homicides are not 
murders. 

Darii. 

All M are S ; 

Some not-P are M ; 
. Some not-P are S ; (or, convert 
. Some S are not P. 
All imprudent acts are foolish ; 



Some not-vicious 
imprudent ; 



acts are 



206 MEDIATE INFERENCE OR SYLLOGISM. 

.*. Some foolish acts are not .*. Some not-vicious acts are 
vicious. foolish ; 

.*. Some foolish acts are not 
vicious. 

These examples show that, after Dokamok has been re- 
duced to Darii, the Conclusion must be contraponed back 
again, if w^e would have it in its original form. 

Ingenious as this whole system of Reduction is, it is 
needlessly artificial and complex. The sole reason for re- 
ducing Syllogisms to the First Figure, we have said, is 
to exhibit the reasoning in its simplest and most natural 
form, and in that in which its validity, or invahdity, is most 
readily perceived. A few simple Rules may be given 
which will enable the learner to accompKsh this object at 
once, in whatever Figure the argumentation may originally 
be propounded, and even without knowing what this Fig- 
ure is. 

1. Every process of reasoning must consist of a Judg- 
ment which is to be proved, and of one or two other Judg- 
ments alleged in its support ; the former is the Conclusion, 
the latter are the Premises. The first step is to reduce 
each of these Judgments to its simplest logical form, — 
that is, to a Subject and Predicate connected by the pres- 
ent tense (affirmative or negative) of the verb to he. Care 
must be taken to determine accurately the Quantity and 
Quality of each of the Judgments. 

2. The Middle Term is that which does not appear in 
the Conclusion. If no such Term is found in the Prem- 
ises, the Inference is Immediate, and must be tried by the 
principles laid down in the preceding chapter, concerning 
Conversion, Opposition, &c. If there is a Middle Term, 
the Inference is Mediate ; then the Major Premise is that 
Judgment in wliich this Middle Term appears connected 
with the Predicate of the Conclusion ; the Minor Premise, 
that in which it is connected with the Subject of the 



CONDITIONAL SYLLOGISMS. 207 

Conclusion. If only one Premise is given in the original 
statement, the other may be easily supplied by a moment's 
consideration, as its two naked Terms are known, and its 
Quantity and Quality may be inferred, through the General 
Rules already given for all Syllogisms, from the Quantity 
and Quality of the Conclusion and the given Premise. 

8. The First Figure requires the Middle Term to be the 
Subject of the Major, and the Predicate of the Minor, 
Premise. If, in the Premises as determined, the Terms do 
not already appear in this order, one or both must be con- 
verted^ either simply, or per accidens, or by Contraposition. 

There can be no difficulty in the application of these 
Rules, which does not arise from some ambiguity in the lan- 
guage of the original statement ; and to resolve such am- 
biguity is the business, not of the logician, but of the gram- 
marian and the lexicographer. But a few cases will be 
incidentally resolved when we come to ti'eat of Fallacies, a 
subject which cannot be fully considered without some- 
times stepping out of the province of Pure Thought. 

2. Conditional Syllogisms. 

Thus far we have treated exclusively of the purely Cate- 
gorical Syllogism, in which each of the component Judg- 
ments can be reduced to one or the other of the two Cate- 
gorical formulas, A is B, or A is not B. The reasoning in 
this case, as we have seen, depends upon the two Axioms 
of Identity and Non-Contradiction. We come now to 
another class of Syllogisms, dependent upon the Axioms 
of Reason and Consequent, and Excluded Middle. 

A Conditional Syllogism is one of which the Major Prem- 
ise, and only the Major Premise, is a Conditional Judgment. 
There are three kinds of such Syllogisms, corresponding to 
the three classes into which Conditional Judgments are 
divided ; namely, the hypothetical^ the Disjunctive, and the 



208 MEDIATE INFERENCE OR SYLLOGISM. 

Dilemmatic or Eypothetico-Bisjunctive. The following are 
examples of each. 

Hypothetical. Disjunctive, 

If A is B, C is D ; A is either B or C ; 
A is B ; A is B ; 

.*. C is D. .-. A is not C. 

Dilemmatic or Hypothetico-Disjunctive. 

If A is B, C is either D or E ; 
C is neither D nor E ; 
.*. A is not B. 

These Terms may be quantified in the Minor Premise, 
as in Categorical Syllogisms, and the Conclusion will still 
be valid, if its proper Quantity be assigned to it according 
to the Rules already given. Thus, if the Minor Premise 
of the preceding Hypothetical be " All A are B," we may 
conclude that '•'•All C are D"; but if we know only that 
" Some A are B," we can only conclude that " Some 
are D." We may likewise use the quantification of Sin- 
gulars, and say, " this A," or " in certain cases, A is B " ; 
then, " in this case," or " in the same cases," C is D. 

Dr. Thomson seems to be wrong, therefore, when he 
gives the following as an instance of a Hypothetical Syllo- 
gism, Figure I. in which each of the three Judgments is 
Hypothetical. 

In cases where M is N, C is D. 

In cases where A is B, M is N. 

In cases where A is B, C is D. 
Here, the supposed Condition, " in cases where A is B," 
is only an awkward quantification of the Minor Premise 
and the Conclusion, equivalent to " in certain cases,^^ or 
" some M is N " ; therefore, in these cases, or some, C is D. 
The reasoning does not turn upon this phrase, " in cases 
where A is B," as a condition, the Consequent being 
evolved from it ; it turns upon it only as a limitation^ 



CONDITIONAL SYLLOGISMS. 209 

showing in how many cases the reasoning is applicable. 
The reasoning does rest exclusively upon the Major 
Premise, where the corresponding phrase, " in cases where 
M is N," 18 a true condition^ the Consequent being evolved 
from it, and the whole argumentation being governed by 
the Axiom of Reason and Consequent. 

This error has led Dr. Thomson into a more serious one. 
Not perceiAang that Hypothetical Reasoning is distinct in 
kind from Categorical, being governed by a different Axiom 
of Thought, he has overlooked the principle that, from 
affirming the Consequent of a Reason, no Conclusion can be 
drawn, and has presented the following as a valid Syllo- 
gism : — 

In cases where C is D, M is N ; 
In cases where A is B, M is N ; 

.*. In cases where A is B, C is D. 
But here the Minor Premise only affirms that " M is N," 
which is the Consequent of the hypothesis in the Major 
Premise ; and therefore the Conclusion is illogical ; the 
Middle Term is not distributed. This can be easily seen 
from the following example, the Conclusion of which is 
evidently a non sequitur. 

If you whip him, the boy cries ; 

If you take away his toys, the boy cries ; 
.'.If you take away his toys, you whip him. 
Then, in a Conditional Syllogism, it is onl^/ the Major 
Premise which is a Conditional Judgment ; for the reason- 
ing turns upon the relation of Reason and Consequent, and 
tliis relation, being once affirmed in the Major Premise, 
affi)rds all the material requisite for the Inference. Both 
the Minor Premise and the Conclusion must be Categorical ; 
the Major contains all the Terms which appear in either of 
them ; whereas, the Minor Premise of a Categorical Syllo- 
gism contains a new Term, which did not appear in the 
Major. If, then, both Premises, or one Premise and Con- 



21U MEDIATE INFERENCE OR SYLLOGISM. 

elusion, are Conditional Judgments, the reasoning is, in 
fact, Categorical, and depends upon the Axioms of Identity 
and Non-Contradiction. This is easily seen in the case of 
a Disjunctive Syllogism, whose form is determined by the 
Axiom of Excluded Middle. 

Every A is either X or Y ; 

But B is A ; 

Then B is either X or Y. 
Here the reasoning is evidently Categorical; the Minor 
Premise introduces a new Term, B, not contained in the 
Major Premise, and therefore the Conclusion is also Dis- 
junctive. 

Endeavoring to prove that, in a Disjunctive Syllogism, 
not only the Major, but the Minor Premise or the Conclu- 
sion, may be a Disjvuictive Judgment, Dr. Thomson pre- 
sents the following as a valid example : — 
C, D, and E are B ; 
C, D, and E = A ; 
.-. A is B. 
This is not a Disjunctive Syllogism at all, as neither of the 
three Judgments is Disjunctive ; the three Concepts which 
constitute the Middle Term are not taken disjunctively, 
but collectively ; that is, one of them does not exclude the 
others, but requires the presence of the others, in order to 
constitute the Predicate. They form one compound Term. 
Thus, let (7, D, and E = M, and make the substitution. 
Then the Syllogism assumes this form, and is evidently 

Categorical. 

MisB; 
M = A; 
.-. A is B. 

The Axiom of Reason and Consequent is explicated, as 
we have seen, into these two principles ; — to affirm the 
Reason or the Condition is also to affirm the Consequent or 
the Conditioned; and to deny the Consequent is also to deny 



CONDITIONAL SYLLOGISMS. 211 

{he Reason. The application of these principles gives us, 
from the same Major Premise, two, and only two, valid 
Moods of the Hypothetical Syllogism, — namely, the 
Modus Ponens and the Modus Tollens. Thus : — 



If A is B, C is D. 



Modus Ponens. 



Modus Tollens. 



C is not D ; 
Then A is not B. 



AisB; 
Then C is D. 
The following are examples of these formulas : — 
Modus Ponkns. 
If matter is essentially inert, every change in it must be 

produced by mind ; 
But matter is essentially inert ; 
Then all changes in it are produced by mind. 

Modus Tollens. 
If the moon shines by its own light, it must always be full ; 
But it is not always full ; 
Then it does not shine by its own light. 

We have said that there are only two valid Moods, be- 
cause, from denying the Reason, or from affirming the Con- 
sequent, nothing follows. The Consequent may foUow from 
some other Reason than the particular one assigned in the 
Major Premise ; and the original Axiom only affirms the 
necessity of some Reason or other, not of any particular 
one. It is true, that the Minor Premise may be quantified 
with the predesignations aZZ, some^ or this, and correspond- 
ing Conclusions will follow. The different forms which 
thus result may, if we please, be called Moods also. 

The Major Premise, or Sumption, in either of the pre- 
ceding examples, may be converted by Contraposition ; 
and the result will be, that what was the Modus Tollens 
becomes the Modus Ponens, and vice versa. These two 
Moods are thus shown to be really one ; and this is pre- 
cisely what we should expect, for the two principles by 



212 MEDIATE INFERENCE OK SYLLOGISM. 

which they are governed are only two explications of one 
Axiom of Thought. Thus, the last preceding example, 
which is now the Modus Tollens, becomes the following, if 
we contrapone the Sumption : — 

If the moon is not always full, it does not shine by its own 

light; 
But it is not always foil ; 
Then it does not shine by its own light. 

Here the Subsumption posits what is now the Reason, 
(though both are negative in form,) and therefore the 
Conclusion posits the Consequent. Hence the reasoning 
has now become the Modus Ponens. 

Summing up what has been said, it appears that the 
Hypothetical Syllogism is subject to these three Special 
Rules : — 

1. It consists of three Judgments, and only three ; but in 
these Judgments there may be more than three Terms. 

2. In respect to Quantity and Quality, the Sumption 
must always be Affirmative and Universal, while the Sub- 
sumption may vary in either of these relations. 

3. The Conclusion is regulated, both in Quantity and 
Quahty, by that member of the Sumption which is not 
subsumed, agreeing with it in both these respects in the 
Modus Ponens^ and differing from it in both in the Modus 
Tollens. 

The Sumption in the last example (after Contraposition) 
may seem not to conform to the second of these Rules ; for 
it appears to be Negative in Quality. But if closely ex- 
amined, the negative particle not will be found to belong 
to each of the two parts (Reason and Consequent) taken 
separately ; while the Sumption, as a whole, affirms the 
connection of these two negative parts with each other. 

Agreeably to what has been said, a Disjunctive Syllogism 
is one of which the Major Premise is a Disjunctive Judg~ 



CONDITIONAL SYLLOGISMS. 213 

ment, while the Minor Premise and the Conclusion are Cate- 
gorical Judgments. The Axiom of Excluded Middle, by 
which this sort of Syllogism is governed, affirms that, of 
two Contradictories i one must be true and the other must 
be false. Accordingly, if the Major Premise presents 
three or more Disjunct Members, the Axiom will not be 
immediately applicable ; these three or more Members are 
only Contraries with respect to each other, and they must 
be reduced to two Contradictories, before we can obtain a 
ground of mference, from positing or sublating one of them, 
to sublating or positing the other. The number of such 
Members can always be thus reduced by considering, for 
the moment, two or more of them as one. After this re- 
duction is accomplished, the Minor Premise and Conclusion 
appear in their true character, not as Disjunctive, but as 
Categorical Judgments. For example : — 



Complete Formula. 
A is either B, C, or D ; 
But A is neither B nor C ; 
Then A is D.* 



Reduced Formula. 

Let BorC= X. 
A is either X or D 
But A is not X ; 
Then A is D. 



This formula, as reduced, presents the universal type of 
Disjunctive reasoning. As its two Disjmict Members are 
Contradictories of each other, the Axiom of Excluded Mid- 
dle authorizes us, from positing either one of them, to sub- 
late the other. This is called the 3Iodus ponendo tollens, 
and it has two forms, according as we posit one or the 
other of the two Disjunct Members. The same Axiom 

* A story is told to illustrate the sagacity of a dog. Following his 
master by the scent, the animal came to a place where three roads met, and 
having ascertained by his nose, at two of them, that the object of his search 
had not taken either of the two, he immediately darted off" by the third, with- 
out pausing to try whether this path also was scentless. The story is un- 
questionably a fiction ; but, if true, the dog must have reasoned by this form 
of the Disjunctive Syllogism, in the modus tollendo ponens. 



214 MEDIATE INFERENCE OR SYLLOGISM. 

permits us, from sublating either of the two, to posit the 
other. This is called the Modus tollendo ponens, and has 
two forms like the other. Hence, every Disjunctive Syllo- 
gism affords, from the same Major Premise, two vahd 
Moods, each containing two forms. It is obvious, that the 
remaining Term, A, of the Major Premise, may be quan- 
tified as all or this, and the Conclusion will appear accord- 
ingly as Universal or Singular. The two Moods and four 
forms of a Disjunctive Syllogism are exhibited in the fol- 
lowing example : — 

Major Premise. Every Judgment is either Affirmative or 

Negative. 

Modus Ponendo Tollens. 
First form. This Judgment is Affirmative ; 

Then it is not Negative. 
Second form. This Judgment is Negative ; 

Then it is not Affirmative. 
Modus Tollendo Pouens. 
First form. This Judgment is not Affirmative ; 

Then it is Negative. 
Second form. This Judgment is not Negative ; 

Then it is Affirmative. 

For those who are fond of mnemonic hexameters, Ham- 
ilton has presented all four forms in the following verses : — 

Ponendo toUens. Fallens aut fallor ; fallor ; non fallen's ergo. 

Falleris aut fallor ; tu falleris ; ergo ego nedum. 
Tollendo ponens. Falleris aut fallor ; non fallor ; falleris ergo. 

Falleris aut fallor ; non falleris ; ergo ego fallor. 

Three Special Rules have been framed for Disjunctive 
Syllogism, though they are so obvious that their formal 
enouncement is hardly necessary. 

1. A regular Disjunctive Syllogism must consist of 
three Judgments only, in which, if the Major Premise 
be reduced to its proper logical form, there can be 



CONDITIONAL SYLLOGISMS. 215 

only tkree Terms, all of which must appear in the Major 
Premise. 

2. The Major Premise must be Universal and Affirma- 
tive ; the Minor Premise may be of either Quality and of 
either Quantity. 

3. The Conclusion must be of the same Quantity, but of 
opposite Quahty, with the Minor Premise. 

Agreeably to what was said in treating of Disjunctive 
Judgments, each Mood of a Disjunctive Syllogism may be 
resolved into a Hypothetical Syllogism, and then its two 
forms appear as the two Moods of the Hypothetical reason- 
ing. For instance, the example last cited may be thus 
transformed : — 

If any Judgment is not Affirmative, it is Negative. 

Modus Ponens, Modus Tollens. 

This Judgment is not Af- This Judgment is not Neg- 

firmative ; ative ; 

Then it is Negative. Then it is Affirmative. 

As a Dilemmatic Syllogism consists of a Hypothetical 
and a Disjunctive combined, and as these two may be com- 
bined in several different ways, the resulting forms are 
numerous and complex. Most of them are really com- 
pound, and a fuU analysis would need to resolve them 
into several simple and subordinate Syllogisms. It would 
be tedious to analyze them all, and this is not necessary, 
as the principles already established for the Hypothetical 
and the Disjunctive Syllogisms taken separately, still gov- 
ern them when taken in connection ; and the learner in 
each case may make the analysis and apply the principles 
for himself. What follows is to be regarded only as illus- 
trating the method to be pursued. 

What has already been presented as a tj'pe of the Di- 
lemmatic Syllogism is, in fact, only a Hypothetical dis- 
guised, as the Disjunction is not resolved, and therefore its 



216 MEDIATE INFERENCE OR SYLLOGISM. 

Disjunct Members, whether two or more, may he regarded 
as a single Term. 

If A is B, C is either D or E. 

MoDtrs PoNENS. Modus Tollens. 

But A is B ; C is neither D nor E ; 

.*. C is either D or E. .•. A is not B. 

In practice, however, the Disjunction is usually resolved, 
in the Modus tollens, by two subordinate (abridged) Syllo- 
gisms, by which it is first separately proved that C is not 7), 
and that C is not E ; and then the Conclusion of the com- 
pound Modus tollens follows, that A is not B. Thus : — 

If man cannot be virtuous, either he must be unable to 
know what is right, or unable to will what is right. 

But he is not unable to know what is right, for he is in- 
telligent ; and he is not unable to will what is right, 
for he is free. 

Therefore, he can be virtuous. 

Hence, .the Dilemma was called by the old logicians 
the Cornutus or horned syllogism, because, in the Sump- 
tion, the Disjunct Members are opposed like horns to the 
assertion of the adversary ; with these, we throw it from 
one side to the other in the Subsumption, m order to toss 
it altogether away in the Conclusion. 

Kmo; remarks : " The Cornutus and Crocodilinus of the 
ancients must not be confounded with the Dilemma which 
we are here speaking of. The former were sophismata 
heterozeteseos, sophisms of counter-questioning ; the latter is 
a legitimate mode of reasoning." But it may be shown 
that the old Cornutus is a legitimate Dilemma in Form, 
and is of the type which we are now considering, the fal- 
lacy being in the Matter. The Litigiosus, for instance, 
which is one illustration of this old fallacy, may be thus 
resolved. 



CONDITIONAL SYLLOGISMS. 217 

Protagoras agi'eed for a large sum to educate Euathlus 
as a lawyer, one half of the price to be paid down, and 
the other half on the day when the pupil should plead and 
gain his first cause. Some time elapsed, and Protagoras, 
thinking that liis disciple intentionally delayed the com- 
pletion of his contract, sued him in court for the remainder 
of the fee, and propounded this Dilemma. 

If Euathlus is to be released from the payment of this 
sum, it must be either because the judgment of this court 
will be in his favor, or against him. 

But if the judgment is in his favor, then he has pleaded 
and gained his first cause, and the money is due me under 
the contract. 

If the judgment is against him, the money is due me 
luider the decision of the court. 

Thus, both the Disjunct Members of the Consequent 
being disproved by subordinate Syllogisms, the Conclusion 
of the compound Modus tollens follows, that Euathlus is 
not to be released from the payment. 

The Dilemma is here correct in Form, but there is a 
Material Fallacy in the Major Premise, since the Disjunc- 
tion is not complete. There is a third horn to it, as Pro- 
tagoras had no right, under the contract, to invoke the 
judgment of the court at all, so that the judges ought to 
have dismissed the case without a hearing. Before a judg- 
ment was rendered^ Protagoras had no ground of action. 

Euathlus is said to have retorted upon his antagonist, by 
propounding a Dilemma in the same Form in which it had 
just been urged against him. " If the decision be favor- 
able to me, I shall pay nothing under the sentence of the 
court ; if adverse, I pay nothing in virtue of the compact, 
because I shall not have gained my first cause." 

" In sifting a proposed Dilemma," says Krug, " we are 
to look closely to the three folloAving particulars : — 
1. Whether, in the Sumption, the Consequent is a legiti- 

10 



218 MEDIATE INFERENCE OR SYLLOGISM. 

mate inference from the Antecedent; 2. Whether the 
Disjunction in the Consequent is complete ; 3. Whether, 
in the Subsumption, the Disjunct Membei'S are properly 
sublated. The following Dilemma is faulty in each of 
these respects. 

" If Philosophy be of any value, it must procure for us 
power, riches, or honor. 

" But it procures neither of them. Therefore, &c. 
" Here, 1. the inference is wrong, as Philosophy may be 
worth something, though it does not secure any of these 
external advantages; 2. the Disjunction is incomplete, as 
there are other goods, besides the three here enumerated ; 
3. the Subsumption is false, as Philosophy has often been 
the means of procuring these very advantages." 

In another form of the Dilemma, the Sumption is a 
Hypothetical Judgment with more than one Antecedent, 
and the Subsumption is a Disjunctive of which these sev- 
eral Antecedents are the Disjunct Members. 

If A is B, C is D ; and if E is F, C is D ; 
But either A is B or E is F ; 
.-. C is D. 
Here, the several Antecedents have the same Conse- 
quent, and therefore the Conclusion is Categorical. If 
they had different Consequents, the Conclusion would be 
Disjunctive. Thus : — 

If A is B, C is D ; and if E is F, G is H ; 
But either A is B or E is F ; 
.♦. Either C is D, or G is H. 
In this case, the Modus tollens is also valid ; if we dis- 
junctively deny the Consequents, we may, in the Conclu- 
sion, disjunctively deny the Antecedents. 

Either C is not D, or G is not H. 
.'. Either A is not B, or E is not F. 
In the preceding case, where the Antecedents had tTie 



DEFECTIVE AND COMPLEX SYLLOGISMS. 219 

same Consequent, if vre deny this one Consequent, we must 
deny the Antecedents taken collectively, and not disjunc- 
tively ; then the Syllogism will be exclusively Hypotheti- 
cal, as neither Judgment will be disjunctive. Thus : — 

If A is B, C is D ; and if E is F, C is D ; 

But C is not D ; 
.*. Then A is not B, and E is not F. 
The nature of a Disjunction is, that any one of the Dis- 
junct Members exists, or is posited, only by the non-exist- 
ence, or sublation, of all the others. Hence, the particles, 
either — or, have a Disjunctive force; but the coiresponding 
negative particles, neither — nor^ have a Conjunctive force, 
as they denote the exclusion of both or all, and not merely 
the exclusion of one on condition of the inclusion of all the 
others. A is either B or C, means that A is B only on con- 
dition that A is not C But A is neither B nor (7, means 
that A is not B and is not 0. 

It has been remarked, that the Modus tollens of the Di- 
lemma, in the form in which it was here first proposed, is 
nothing but a Negative induction. 

If A is B, C is either D, E, or F ; 

But C is neither D, E, nor F ; 

Then A is not B. 
This can be resolved into a Categorical Syllogism of 
Induction. Thus : — 

C is not D, is not E, and is not F ; 

But these are all the possible cases of A being B ; 

Then A is not B. 

8. Defective and Complex Syllogisms. 

It has already been mentioned, that men do not usually 
speak or write complete Syllogisms ; nay, it is almost only 
in treatises on Logic that we find Syllogisms completely 



220 MEDIATE INFERENCE OR SYLLOGISM. 

enounced, or with all their parts expressed. The abridged 
form is preferred on all ordinaiy occasions, because at least 
one of the three Judgments is so obvious, both to the 
speaker and the hearer, that it would be a waste of time 
and words — a sin against brevity, and even against per- 
spicuity — to pi'opound it openly; for unnecessary words 
do not elucidate, but obscure, the Thought. We usually 
express a single process of reasoning by two Judgments, 
connected by an illative particle, because, then, therefore^ 
&c. ; sometimes only by a conjunctive particle, and. The 
following are instances of reasoning thus enounced. 

Aldebaran is a star ; therefore, it shines by its own light. 
No avaricious person can be happy ; because he who is 

never free from fear cannot be happy. 
A liar ought not to be believed; and this witness has been 

proved to be a liar. 

Such sentences as these are called Enthymemes, because 
they are abridged statements of a process of reasoning, one 
of the three Judgments necessary to constitute the Syllo- 
gism being Iv 6vfia>-, in the mind, but not expressed. In 
the first case, the suppressed Judgment is the Major Prem- 
ise, — all stars shine hy their own light ; in the second, it 
is the Minor Premise, — an avaricious person is never free 
from fear, the Conclusion also, as is frequently the case in 
Enthymemes, being placed first, instead of last ; in the 
third case, the suppressed Judgment is the Conclusion, — 
this wit7iess ought not to be believed. 

An Enthymeme, then, is not a pecuhar kind of Syllo- 
gism, but only an abridged expression of a Syllogism. Of 
course, the doctrine of Enthymemes properly belongs, not 
to Logic, but to Rnetoric, for it concerns expression, not 
thought ; and it would never have been obtruded into the 
former science but for the authority of Aristotle, who em- 
ployed the name, mdeed, m a different and now disused 



DEFECTIVE AND COMPLEX SYLLOGISMS. 221 

meaning, signifying by it " a reasoning from signs and like- 
lihoods." 

Hitherto, we have treated only of the so-called Mono- 
syllogism^ — that is, of a Syllogism considered as one in- 
dependent whole, without reference to the continuous chain 
of reasoning, of which, in an abridged form of expression, 
it usually constitutes a single link. Many truths — most 
of the theorems in Geometry, for instance — can be 
proved only by a Chain of Reasoning ; — that is, by a 
connected series of Syllogisms, the several portions of 
which are dependent upon each other. A Conclusion of 
one may become a Premise of the next succeeding Syllo- 
gism, and is then called, in reference to its successor, a 
Prosyllogism ; while the latter, in reference to the one 
which preceded it, is called an Episyllogism. A Prosyllo- 
gism, then, is a Syllogism whose Conclusion is a Premise of 
that which follows ; and an Episyllogism is one whose Prem- 
ise is a Conclusion of that which precedes. As, in a hierarchy 
of Concepts, the same class-notion is at once a Genus to 
the class below and a Species to the class above ; so, in a 
Chain of Reasoning, the same Syllogism is at once a Pro- 
syllogism and an Episyllogism in its opposite relations. 
Only that which contains the primary or highest reason 
can be exclusively called a Prosyllogism ; only that which 
enounces the last or lowest consequent is exclusively an 
Episyllogism. 

The Syllogism constituting a Chain may be either partly 
complete and partly abbreviated, or all equally abbreviated. 
In the former case, the complex Syllogism which results is 
called an Epicheirema ; in the latter, it is called a Sorites. 

A Syllogism is called an Epicheirema, when, to either or 
both of its two Premises, there is attached a reason for its 
support. The Premise with such a rider annexed is, in 
fact, a Prosyllogism abbreviated, — that is, an Enthymeme 
used to prove one of the branches of the main Syllogism. 
Thus : — 



, I 

I 



222 



MEDIATE INFERENCE OR SYLLOGISM. 



M is P ; The flesh of ruminants is good for 

food ; 
S is M, because it is N ; These animals are ruminants, be- 
cause they have cloven hoofs ; 
.*. S is P. .'. These animals are good for food. 

Here, the Enthymeme, wliich is a rider of the Minor 
Premise, may be thus explicated into a complete Prosyllo- 
gism. 

All animals which havo cloven hoofs are ruminant ; 
These animals have cloven hoofs ; 
.*. These animals are ruminants. 

It has already been said, that every Syllogism may be 
regarded as an application of the general and self-evident 
principle, that a part of a 'part is a part of the whole. If, in 
the application of this principle, we do not stop at the first 
or proximate whole, but, before drawing any expressed Con- 
clusion, proceed step by step to remoter parts and more 
comprehensive wholes, and, in the Conclusion, finally place 
the smallest part under the largest whole, the complex 
abbreviated reasoning thus formed is called a Chain-Syllo- 
gism, or /Sorites. It may be aptly symbolized by a series 
of concentric circles. 



1. AisB 

2. B is C 

3. C is D 

4. DisE 
Therefore, A is E. 



A Sorites of this sort may be described as a series of 
Entliymemes with siippressed Conclusions, in which the Pred- 
icate of each is the Subject of the next, and the Conclusion 
of the whole is formed from the first Subject and last Pred- 
icate of the Premises. The Conclusion being thus formed, 




DEFECTIVE AND COMPLEX SYLLOGISMS. 223 

it is evident that there must be as many Middle Terms 
(i. e. Terms intervening between the first Subject and last 
Predicate, that is, again, between the smallest part and the 
greatest whole which the reasoning connects) as there are 
Premises minus one ; consequently, every Sorites may he 
explicated into as many distinct Syllogisms as there are 
Premises minus one. The first Judgment in the Sorites is 
the only Minor Premise that is expressed ; each of the 
other Minor Premises is the Conclusion of the separate 
Syllogism next preceding. Hence, each of the Judgments 
in the Sarites except the first is the Major Premise of a 
distinct Syllogism. The preceding Sorites, for instance, 
may be thus explicated into three Syllogisms, the correct- 
ness of the explication being made very evident by a refer- 
ence to the diagram. 



I. 


II. 


III. 


2. B is C, 


3. C is D, 


4. D is E, 


1. A is B ; 


A is C ; 


A is D ; 


.-. A is 0. 


.-. A is D. 


.'. A is H. 



An invalid Mood occurring anywhere in the series 
before the last Syllogism would not only be wrong itself, 
but, as furnishing a Premise to its successors, would vitiate 
all that follow. Hence, in a Sorites, out of all the Prem- 
ises, only the one first expressed may be Particular ; be- 
cause, in the First Figure, to which all the separate Syllo- 
gisms belong, the Minor Premise may be Particular, but 
not the Major; and all the Judgments in the Sorites, 
except the first and the Conclusion, are Major Premises. 
In the Sorites, also, only the last Judgment may be Nega- 
tive ; for if any other of its Judgments were Negative, the 
Syllogism formed from the next following Judgment would 
have a Negative Minor Premise, which the First Figure 
does not admit. A Sorites in the Modus tollens, then, can 
be stated only in one form ; — from denying the last Con- 



224 MEDIATE INFERENCE OR SYLLOGISM. 

sequent of the last Antecedent, we go back to denying 
this same Consequent of the first Antecedent. Thus, if 
we say that D is not E, we must conclude that A is not ^. 
The three distinct Syllogisms already given are not all 
that may be formed from the given Sorites. Instead of be- 
ginning with the first Judgment, and thereby finally con- 
cluding that A is -E^, we may begin with the second Judg- 
ment, first concluding that B is D, and then that B is E ; 
and again, beginning with the thirds we may conclude that 
C is JE. Hence, fi'om a Sorites with four Premises, we 
may form in all six distinct Syllogisms. If there were five 
Premises, there would be ten resultant Syllogisms, " The 
formula," says Dr. Thomson, " for ascertaining the num- 
ber of Conclusions is this : — Let the number of Premises 
= n ; the number of terms = w -f- 1 j then the number 
of Conclusions = — — ~ 

Goclenius invented another form of the Sorites, to which 
his name has been attached ; it is the same as the common 
form, except that the Premises are reversed. Referring to 
the diagram again, it is evident that, instead of beginning 
with the Terms of least Extension, represented by the in- 
nermost circles, we may begin with the more Extended 
Terms in the outer circles. Then the Subject of each 
Judgment becomes the Predicate of the next; while, in 
the common form, it is the Predicate of the former which 
becomes the Subject of the latter. The Goclenian Sorites 
is thus stated : — 

DisE, 

C is D, 

BisC, 

AisB; 
.-. A is E. 

Here, Extension is more prominent, as we start with the 
wider Terms ; hence, this form is better suited for deduc- 



DEFECTIVE AND COMPLEX SYLLOGISMS. 225 

tion. In the common form, Intension predominates, as 
the narrower Terms come first; Induction natm'ally as- 
sumes this Form. 

" A ' pretty quarrel ' long existed amongst logicians," 
says Dr. Thomson, " which of the two was to be called 
progressive and which regressive. It was a mere strife 
about words. If we are discovering truth by the inductive 
method, the Aristotelian form is progressive ; if we are 
teaching tnith, or trying our laws upon new facts, we use 
deduction, and the Goclenian form is progressive. In an 
apt but familiar figure, — if I am on the ground floor, and 
wish to fetch something that is above, my going up stairs is 
my progress towards my object, and my coming down is a 
regression ; if the positions of myself and the thing are re- 
versed, going down would be progress, and returning up, 
regress. The inductive truth-seeker is on the ground-floor 
of facts, and goes up to seek a law ; the deductive teacher 
is on a higher story, and carries his law down with him to 
the facts. 

*' This will be clearer from a pair of examples. 

Goclenian or descending Sorites. Aristotelian or ascending Sorites, 

Sentient beings seek happiness ; Caius is a man ; 

All finite beings are sentient ; All men are finite beings ; 

All men are finite beings ; All finite beings are sentient ; 

Caius is a man ; All sentient beings seek happi- 
ness ; 

Therefore Caius seeks happi- Therefore Caius seeks liappi- 

ness. ness." 

By way of recapitulation, the chief principles and rules 
of the Aristotelic doctrine of Syllogism are brouglit to- 
gether in the following Conspectus. 



10 • 



226 



CONSPECTUS OF THE ARISTOTELIC 



Mediate Infehekce or Stllo- 

GISM 

is that act of Thought whereby the 
relation of the two Terms of a pos- 
sible Judgment to each other is 
ascertained by comparing each of 
them separaiely with a Third Term. 



Syllogisms 

Categorical, 

in which each of the three Judgments can be 
expressed under one or the other of these 
two Formulas : — 

A is B : A is not B. 



Gekeral Canon 

of Categorical Syllogisms. In so far 
as two Notions, (Concepts or Indi- 
viduals,) either both agree, or, one 
agreeing, the other does not agree, 
with a common Third Notion, in 
so far these Notions do, or do not, 
agree with each other. 



This Canon is explicated 

n. 



A Syllogism must 
contain three Terms, 
and no more. 



A Syllogism must 
contain three Judg- 
ments, and no more. 



The Figuee 

of a Syllogism is determined by the 
relative position of the Middle Term 
in the two Premises. 



Let S = Subject of the 



Figure I. MP; 
SM; 
.'.SP. 



The Mood 

of a Syllogism is the value of its three 
Judgments in respect to their Quan- 
tity and Quality, as indicated in 
each case by the four Judgments, 
A, E, I, and O. 



Valid 



Fig. I. 
AAA; Barbara. 
£ A E ; Celarent. 
A I X ; Darii. 
E I O i Ferio. 



Reduction 

of the valid Moods of the three lower 
Figures to those of the First Fig- 
ure may be accomplished by per- 
forming the processes indicated by 
the following letters in the names 
of those Moods. 



B = Reduce the Mood to Barbara. 
C = " " Celarent. 

D = " " Darii. 

F= " " Ferio. 



Geneeal Canon 

of Hypothetical Syllogisms. To aflBrm 
the Reason or the Condition is to 
aflBrm the Consequent ; and to deny 
the Consequent is also to deny the 
Reason. 



This Canon produces, from 
Major Premise, 



Modus Ponens. 
A is B ; 
.'. C is D. 



General Canon 

of Disjunctive Syllogisms. Of two 
Contradictories, one must be true 
and the other must be false. 



This Canon produces, firom 

Major Premise, 

Modus ponendo tollens. 

1. A is B ; 

.'. A is not C. 

2. A is ; 

.'. A is not B. 



DOCTRINE OF SYLLOGISM. 



227 



ARE EITHER 



OR Conditional, 



in which the Major Premise, and only the Major Premise, is a Conditional Judgment ; an4 
these are subdivided into 



Hypothetical i 
Major Premise, 
If AisB, CisD. 



Disjunctive ; 
Major Premise, 
A is either B or C. 



Dilemmatic or Hypotheti' 
cat Disjunctive. 
Major Premise, 
M A is B, C is either D or E. 



into these six Oeneral Eules. 

in. 



The Middle Term 
must be distributed 
in at least one of the 
Premises. 



IV. 



One Premise at least 
must be Al£rmatire. 



If either Premise is 

Negative, the Con- 
clusion most be Neg- 
ative. 



VI. 

Neither Term must 
be distributed in the 
Conclusion, if it was 
not distributed in 
the Premise. 



Conclusion ; P = Predicate of the Conclusion ; M = Middle Term. Then, 



Figure IL P M ; 


Figure III. MP; 


Figure IV. PM; 


SM; 


MS; 


MS; 


.-.SP. 


.-. S P. 


.-.SP. 



Moods. 

Fig. n. 

E A E ; Cesare. 
A E E ; Camestres. 
E 1 O ; Festi7io. 
A O O ; Baroko (Fakoro). 
All Negative Conclusions. 



Fig. rti. 
A A I ; Darapti. 
I A I ; Disamis. 
All; Datisi. 
£ A O ; Felapton. 
O A O ; Bokardo {Dokamok). 
E I O. Ferison. 
All Particular Conclusions. 



Fig. IV. 
A A X ; Bramantip, 
A E E ; Cameves. 
I A I ; Dimaris. 
E A O ; Fesapo. 
E I O ; Fresison. 



m = Transpose the Premises, 
s = Convert simply. 
p = Convert />er accidens. 
k = Reduce per impossibile for 
Baroko & Bokardo ; 
Convert by Contraposition for 
Fakoro & Dokamok. 



Barbara, Celarent, Darii, Fertoque, prioris ; 
Cesare, Camestres, Festino, Baroko, secundae ; 
Tertia Darapti, Diaamis, Datisi, Felapton, 
Bokardo, Ferison habet ; Quarta insui)er addit 
Bramantip, Camenes, Dimaris, Fesapo, Fresison. 



the same Premise, two valid Mooda. 

If AisB, CisD. 

Modus Tollens. 

C is not D ; 
.*. A is not B. 



the same Premise, two valid Moods, each having two forms. 

A is either B or C. 

Modus tollendo ponena. 

1. A is not B ; 
.-. A is C. 

2. A is not C ; 
.-. A is B. 



228 MEDIATE INFERENCE OR SYLLOGISM. 



CHAPTER VIII. 

THE HAMILTONIAN DOCTRINE OF SYLLOGISMS. 

SIR William Hamilton's innovations in the doctrine 
of Syllogisms, which had been generally received 
up to this time, are not limited to such as are the direct 
consequences of his theory of the thorough-going quanti- 
fication of the Predicate. On several minor points, also, 
he has considerably modified the Aristotelic doctrine. 
These changes, it is true, were probably suggested by his 
system of quantifying the Predicate ; but they are not so 
closely connected with it as to prevent them fi-om being 
received, even by those logicians who, wholly or in part, 
reject that system. All of them deserve consideration, as 
they involve a discussion of some incidental questions of 
much interest, affecting the whole theory of Logic. 

As to the order of enouncement, the old doctrine was, 
that the Premises, as their name imports, should precede 
the Conclusion. Hamilton observes that the reverse order 
is more natural, that it more faithfiilly represents the 
progress of the mind in the investigation or discovery of 
tnith, and that it effectually relieves the Syllogism from 
the imputation, which has been thrown upon it for more 
than three centuries, of being founded upon a mere petitio 
principii, or a begging of the question. " Mentally one," 
he says, " the Categorical Syllogism, according to its order 
of en<*^,mcement, is either Analytic^ if what is inappro- 
priately styled the ' Conclusion ' be expressed first, and 
what are inappropriately styled the ' Premises ' be then 



THE HAMILTONIAN ANALYSIS. 229 

stated as its reasons ; or Synthetic^ if the Premises precede 
and, as it were, effectuate the Conclusion." In the Ana- 
lytic order, the " Conclusion " would be more properly 
called the Qitcesitum, and the "Premises" should be 
denominated the Proofs. 

Now, the Analytic order, it is argued, is the more nat- 
ural, because the Problem or Question, which it is the 
purpose of the Syllogism to solve or answer, and which is 
therefore the leading thought in the mind, is propounded 
first. When we are in doubt whether A is, or is not, B, 
it is surely more natural to argue, A is B, because A is C, 
and all is B, than to reason in the old order, placing the 
solution of the Problem last. " In point of feet, the Ana- 
lyvic Syllogism is not only the more natural, it is even pre- 
supposed by the Synthetic." As already stated, the Syllo- 
gistic process in the mind is really one and undivided, con- 
sisting only in the inference of the Conclusion from the 
Premises. But in order to state this single process in 
words, we must analyze it, and therefore the Conclusion, 
which is the compound result, ought to be stated first, so 
as to admit of analysis. It may be stated generally, that a 
process of investigation or research, looking towards truth 
not yet discovered, is always Analytic. The most that can 
be said for the Synthetic method is, that it may be suc- 
cessfully used for teaching, or proving the truth that is 
already known. To adopt an old illustration, in order to 
find out for ourselves how a clock is made and how it does 
its work, we must take it to pieces ; having done this, the 
best way to teach another person how to make a clock is 
to take those pieces and put them together again. 

The common objection to the validity of the Syllogistic 
process is, that the Conclusion is virtually contained in the 
Premises, so that we have to assume it to be true in the 
very propositions by which we attempt to prove it. This 
objection is thus forcibly stated by Mr. Mill. " When we 
say, — 



230 MEDIATE INFERENCE OR SYLLOGISM. 

All men are mortal ; 

Socrates is a man ; 

Therefore, Socrates is mortal ; 
it is unanswerably urged by the adversaries of the Syllo- 
gistic theory, that the proposition, ' Socrates is mortal,' is 
presupposed in the more general assumption, ' All men 
are mortal ' ; that we cannot be assured of the mor- 
tality of all men, unless we were previously certain of 
the mortality of every individual man ; that if it be still 
doubtful whether Socrates, or any other individual you 
choose to name, be mortal or not, the same degree of un- 
certainty must hang over the assertion, ' All men are 
mortal ' ; that the general principle, instead of being given 
as evidence of the particular case, cannot itself be taken 
for true Svithout exception, until every shadow of doubt 
which could affect any case comprised with it is dispelled 
by evidence aliunde ; and then, what remains for the Syl- 
logism to prove ? that, in short, no reasoning from generals 
to particulars can, as such, prove anything : since, from a 
general principle, you cannot infer any particulars but those 
which the principle itself assumes as foreknown." 

But if the Syllogism be stated in the Analytic form, 
it is obvious that this objection is inapplicable. When we 
argue, — 

Socrates is mortal. 

Because Socrates is a man, 

And all men are mortal, — 
we do not assume the point which ought to be proved, but 
we prove that it is right to predicate mortality of Socrates, 
by showing that Socrates belongs to the class man^ all the 
members of which are universally admitted to be mortal. 
We appeal to the admitted Universal truth only after we 
have established, what is here the main point of the argu- 
ment, the applicability of the truth to this case, — the fact 
that Socrates is a man. Mr. Mill mistakes the compara- 



THE HAMILTONIAN ANALYSIS. 231^. 

tive importance of the two Premises ; in Analytic reason- 
ing, — in drawing an inference for the purpose of investi- 
gation or discovery, — the proof turns chiefly upon the 
Subsumption ; and Aristotle therefore correctly places this 
Premise first. Thus, if I am in doubt with respect to a 
new substance which I have found, whether it be fusible or 
not, the doubt may be resolved by ascertaining that tliis 
substance is a metal. Only after this fact is ascertained, 
and then only in order to complete the thought, or to si- 
lence cavil, I refer to the admitted truth that all metals are 
fusible. Men usually reason in this manner, as is shown 
by the frequent recurrence of such Enthymemes as these : 
This iron is not malleable, for it is cast-iron ; The man is 
dishonest, for he has taken what is not his own ; this line is 
equal to that, for they are both radii of the same circle, &c. 
There is certainly a mental reference in such cases to a 
Major Premise, — to the well-known truths, that iVb east- 
iron is malleable. All radii of the same circle are equal, &c. 
But precisely because such Premises are well known and 
obvious, though thought, they are not usually expressed. 

The bald truisms which are usually taken as examples 
of the Syllogistic process are unfortunately chosen, as they 
render more plausible the imputation that this process itself 
is futile and needless. Any kind of reasoning appears 
puerile, when it is applied only to establish a puerile Con- 
clusion. Nobody wishes any proof of the fact that Soc- 
rates was mortal. Adopt any supposition which will make 
it appear that there was a real doubt in the case, and that 
the point to be determined was one of some importance, 
and the Syllogism employed loses its fi'ivolous aspect, and 
seems grave and pertinent. Suppose that the impulsive 
Athenians of his day had made the same mistake in rela- 
tion to Socrates, that those of a later time committed in 
regard to Paul and Barnabas, and had begun to offer sac- 
rifices to him as an immortal being ; it would have been 



232 MEDIATE INFERENCE OR SYLLOGISM. 

dignified and conclusive on his part to argue with them, as 
the Apostle did, by saying, " We are men of like passions 
with you," and worship is due only unto God. The first 
question for the inquirer or disputant is, not whether this 
case has already been decided, and therefore included 
under this General Rule, which is supposed to be already 
found ; but under what Class-notion can this case be put, 
which shall afford a General Kule that will be applicable 
for the solution of the doubt. The difficulty is, how to 
find the right Rule, and not, as Mr. Mill supposes, how to 
interpret it when found. The astronomer proceeds in this 
manner, when he seeks to know whether a comet, which 
has just appeared in the heavens, will return at a future 
period, or disappear forever. By determining three or 
more points in its path, he ascertains either that its orbit is 
an ellipse or an hyperbola; this is the Subsumption, and 
when found, the question is really answered, for the appli- 
cation of the Sumption — that the ellipse is a curve which 
returns into itself, while the hyperbola does not — is so 
obvious, that it is unnecessary, except for a child, to be 
reminded of it. But though not expressed, the thought 
without it is certainly incomplete, and the main question is 
not answered. 

Mr. Mill's doctrine is, that " we much oftener conclude 
from particulars to particulars directly, than through the 
intermediate agency of any general proposition." For ex- 
ample, " it is not only the village matron, who, when 
called to a consultation upon the case of a neighbor's child, 
pronounces on the evil and its remedy simply on the rec- 
ollection and authority of what she accounts the similar 
case of her Lucy." 

We have already observed (page 9) that a Concept may 
be derived from one object, as well as fi-om many similai 
ones ; that is, it may not represent an actual, but only a 
possible, class or plurality of things. The hasty and sweep- 



THE HAMILTONIAN ANALYSIS. 233 

ing inductions of the vulgar are of this character ; thej are 
often ffenerahzations from a single instance. The medicine 
which they have once successfully tried is believed by them 
to be a panacea. The unhesitating confidence with which 
the village matron pronounces, not merely on one case of 
measles or whooping-cough in her neighbor's family, but 
on every one that occurs in the village, proves that she 
has generalized her Lucy's case. 

All general truths are not learned by induction from 
particulars. They are sometimes first obtained by Intu- 
ition, as in the case of axioms and other necessary tiniths, 
or by reasoning from the causes or conditions on which 
they depend; and then, individual truths are proved by 
deduction fi'om these generals. Most of the truths of pure 
mathematics are thus acquired. To borrow an example 
from Hobbes, — because we know how a circle is gener- 
ated, namely, by the circumduction of a body one end of 
which is fixed, we know that all radii of the same circle 
are equal. Most of the beautiful applications of algebraic 
theorems to the solution of arithmetical and geometrical 
problems were first ascertained to be possible long after the 
general theorems themselves were discovered. Such meta- 
physical principles as these. Every event must have a cause^ 
All attributes presuppose a suistance. Space is infinite and 
indestructible^ were not first made known to us by induc- 
tion, and cannot be proved by that method. Yet the ob- 
jection to the Syllogistic process, that the Major Premise 
could not be posited if the truth of the Conclusion were 
not already known, has neither force nor relevancy, if it 
be not proved'that all general truths are obtained by in- 
duction, and that the induction was so perfect that it must 
have consciously included the very case which we are now 
seeking to deduce from the general rule. 

Hamilton's next innovation in the theoiy of Logic — 
and it is one which was propounded by him at an earher 



234 MEDIATE INFERENCE OR SYLLOGISM. 

day than liis doctrine of the quantification of the Predicate 
— was to draw attention to the fact, that reasoning does 
not proceed, as had formerly been taught, solely in the 
Quantity of Extension, but also in the Quantity of Inten- 
sion, the relations of whole and part, on which he considers 
that the whole process depends, being reversed in these 
opposite Quantities. It has already been mentioned, that, 
in one sense, the Predicate of every Judgment includes the 
Subject, and therefore, as the greater or more Extensive 
Term, it was called the Major, and the Subject was desig- 
nated as the Minor Term. As thus construed, the Judg- 
ment, 3Ian is an animal, means that the class 3fan is ui- 
cluded under, or forms a part of, the class animal. But in 
another sense, — that is, in the Quantity of Intension, — 
the Subject includes the Predicate, and the relations of 
whole and part are reversed. Interpreted Intensively, this 
Judgment signifies that all the attributes of animal are 
contained in or among — form a part of — the attributes of 
man. The Subject is now the Major Term, and the Pred- 
icate is the Minor ; and the rule being stiU adhered to, that 
the Major Premise must be stated first, the order of the 
Premises is reversed. 

Hamilton gives the following example of reasoning in 
Extension. 

All responsible agents are free agents ; 

But man is a responsible agent ; 

Therefore, man is a fi-ee agent. 
The Premises are stated in this order on the supposition 
that *'free agents," as the more Extensive class, is the 
whole or the Major Term, that " man," having the least 
Extension, is the smallest part or the Minor Term, and 
that the Middle Term, " responsible agent," as interme- 
diate between the two, is made the Subject of the former, 
as contained under it, and the Predicate of the latter, which 
is only a part of it. In other words, man is a part of that 



THE HAMILTONIAN ANALYSIS. 235 

Term responsible agent^ which is itself a part of the Term 
free agent ; and therefore, as a part of a part is a part of 
the wliole, man is a free agent. 
Now reverse the Premises. 

Man is a responsible agent ; 

But a responsible agent is a free agent ; 

Therefore, man is a free agent. 
Here, the notion /ree agent, which was the greatest whole, 
becomes the smallest part ; and the notion man, which was 
the smallest part, becomes the gi*eatest whole. " The 
notion responsible agent remains the Middle quantity or 
notion in both, but its relation to the two notions is re- 
versed ; what was formerly its part being now its whole, 
and what was formerly its whole being now its part." 

Hence, in the First Figure (but not, as we shall see, in 
the two other Figures), the order in which the two Prem- 
ises are placed always indicates the Quantity in which we 
are reasoning. If the Major Premise contains the Subject 
of the Conclusion, then this Subject is the Major Term, and 
the reasoning is in Intension. But if the Predicate of the 
Conclusion appears in the first Premise, then this Predicate 
is the Major quantity, and the reasoning is in Extension. 

But as this indication is a faint one, and may mislead in 
the case of the Second or the Third Figure, it is easy to 
change the pliraseology of the Judgments, so as to enounce 
explicitly whether the reasoning concerns the Intensive, 
metaphysical, whole (the whole of the Marks connoted), or 
the Extensive, logical, whole (the whole of the Indi^aduals 
and Species denoted). Thus, for the latter, we may say, — 

All responsible agents are included in the class of free 

agents ; 
But man is a responsible agent ; 
Therefore, man is included in the class of free agents. 

And the reasoning of Intension mav be thus stated : — 



236 MEDIATE INFERENCE OR SYLLOGISM. 

The notion or Concept, man, includes the notion of respon- 

sibiUty ; 
But the notion of responsibihty includes that of free 

agency ; 
Therefore, the notion, man, includes the notion of free- 
agency. 
It is the more remarkable that nearly all the logicians 
since Aristotle should have contemplated exclusively rea- 
soning in Extension, as Aristotle himself seems to have 
regarded reasoning in Intension as coextensive with the 
former, even if not paramount to it. Hamilton has only 
restored the doctrine of the great founder of Logic, which 
had been strangely overlooked by nearly the whole tribe 
of his commentators and followers. As afready remarked, 
the being in a Subject and the being predicated of a Sub- 
ject are used by Aristotle as synonymous phrases. " A 
is predicated of all B," means All B is A ; " -4 is in (or 
inheres in^ virapx^i'v) all £" also means All B is A. 
The meaning evidently is, that, in the Quantity of Inten- 
sion, the Predicate is in the Subject because it constitutes 
a part, and only a part, of the Intension of the Subject. 
Animal is in man, because man has all the attributes or 
Marks of animal, and other attributes also. 

But the relation of whole and part is not precisely the 
same thing in the one Quantity as in the other. In Exten- 
sion, the whole is the Genus, and the parts are the subor- 
dinate Species ; and the first Rule for the division is, that 
the parts, or the co-ordinate Species, must exclude each 
other. But in Intension, the parts are not Species, but 
attributes or Marks ; and these do not exclude each other. 
Each part or attribute here interpenetrates, so to speak, 
and informs, the whole. Black is a part of negro in the 
sense of being only one of his attributes, since he has many 
others, such as being long-heeled, prognathous, &c. ; but it 
is a part which colors the whole, for the negro is black all 



THE HAMILTONIAN ANALYSIS. 237 

over. But if we consider the Extension, if the Genus man 
is subdivided into the co-ordinate Species white man and 
black man^ these parts exclude each other; no one man 
can belong at the same time to both Species, — can be both 
white and black. 

Hence the maxim, that a part of a part is also a part of 
the whole, is not a universal maxim of all reasoning ; as it 
refers only to co-exclusive parts, it is applicable only to 
reasoning in Extension. The corresponding maxim for 
reasoning in Intension is, that a Mark of a Mark is also a 
Mark of the thing itself, — of the whole thing ; nota notce 
est nota rei ipsius. Free agency, which is a Mark of 
responuhility, is also a Mark of man, because responsibility 
is a Mark of the whole man. On the other hand, reason- 
ing Extensively, we say, men are a part or class of respon- 
sible agents, and are, therefore, also a part o^ free agents^ 
because responsible agents are a part oi free agents. 

By not attending to this distinction, Hamilton was be- 
trayed on one occasion into propounding as a valid syllo- 
gism one, which, if the language be construed literally, is 
illogical ; and into censuring as illogical another, which, as 
stated, is certainly irrecusable. It is true that the error 
consisted entirely in the use of language. As he under- 
stood them, his approbation of the one and his censure of 
the other are correct ; but from his use of language, no 
other person would so understand them. In his Lectures 
on Logic, while illustrating the Special Rule of an Inten- 
sive Syllogism (page 223, Am. ed.), that the Sumption 
must be Affirmative, and the Subsumption Universal, he 
states the following as a valid Syllogism : — 



" S comprehends M ; 
M does not comprehend P ; 
Therefore S does not comprehend P." 





238 MEDIATE INFERENCE OR SYLLOGISM. 

If the language be interpreted literally, the Conclusion 
here is illogical ; for it is evident, from the diagram which 
we have annexed, that, though S comprehends 31, and M 
excludes P, it may yet be true that S comprehends P. 

On the same page, he censures the following as a nan 
sequitur, though the diagram here annexed demonstrates it 
to be valid. 

S does not compre- 
hend M ; 

But M comprehends P ; 

Therefore S does not 
comprehend P. 

But instead of the proposition " S comprehends M," sub- 
stitute the meaning which was intended, that S has M for 
one of its Marks or attributes, and make the corresponding 
change throughout, and Hamilton's verdict upon the two 
Syllogisms becomes correct. M, though only one of the 
attributes of S, affects or colors the whole of S ; therefore, 
P, which is not an attribute of M, — does not affect any 
part of M, — is not an attribute of S ; — S does not in- 
clude P among its attributes. The Syllogism which is ap- 
proved corresponds, in Form, to the following, which is 
evidently valid. 

A negro has a black skin ; 

But a black skin is not an invariable sign of a brute in- 

tellect ; 
Therefore, a negro is not necessarily brutish in intellect. 

And the Syllogism which is rejected is the following : — 
A negro is not white ; 
But whites are civilized ; 
Therefore, a negro is not civihzed. 

In fact, the mode of symbolizing Syllogisms by circles, as 



THE HAMILTONIAN ANALYSIS. 239 

well as the maxim, a part of a part is also a part of the 
whole^ is inapplicable to the Intensive Syllogism ; for here 
the " parts " are Marks or attributes ; and these are not 
co-exclusive. They are not partes extra partes. 

It is with some reason, then, that Mr. DeMorgan objects 
to considering the Intension of a Concept as a quantity. 
In the vague sense of being susceptible of more and Zess, it 
is a quantity ; but so far as it is incapable of exact measure- 
ment^ it is not a quantity. " As to extent," he says, " 200 
instances bear a definite ratio to 100, which we can use, 
because our instances are homogeneous. But different quali- 
ties or descriptions can never be numerically summed as 
attributes to any purpose arising out of their number. 
Does the idea of rational aniynal, two descriptive terms, 
suggest any useful idea of duplication^ when compared with 
that of animal alone ? When we say that a chair and a 
table are more furniture than a chair, which is true, we 
never can cumulate them to any purpose, except by ex- 
tracting some homogeneous idea, as of bulk, price, weight, 
&c. To give equal quantitative weight to attributes, as 
attributes, seems to me absurd ; to use them numerically 
otherwise, is at present impossible." Perhaps this is only 
saying that a logician's idea of quantity is not the same as 
a mathematician's ; to the latter, it is always numerically 
definite, or may be made so ; to the former, it is never so. 
Perhaps, if Mr. DeMorgan had kept this fact steadily in 
view, a good many of his attempted innovations in Logic 
might have appeared, even to him, irrelevant. 

Hamilton has made no specific innovation in the doctrine 
of the Figures, but his speculations upon the subject have 
thrown a flood of light not only upon the essential nature 
of these varieties of the Syllogism, but upon the theories 
of former logicians in respect to them. To Aristotle, on 
account of his peculiar method of stating a Judgment, — 
with reference to the Intension instead of the Extension of 



240 MEDIATE INFERENCE OR SYLLOGISM. 

its Terms, that is, placing the Predicate first and the Sub- 
ject last, — the Middle Term was intermediate between 
the two others, not only in nature, but in position. Thus, 
the following are only two different expressions of the same 
Syllogism. 

Aristotle's form. Later or common form. 

P inheres in (is predicated of) all M ; All M are P ; 
M inheres in all S ; All S are M ; \ 

.'. P inheres in all S. .*. All S are P. 

Here, in Aristotle's form, P, one of the Extremes, appears 
first, and S, the other Extreme, comes last ; M, the Middle 
Term, in both of its expressions, being intermediate, or 
coming between them. In the later form, it is not so. 
As a consequence of this mode of statement, in his defini- 
tion of the Second Figure, Aristotle says that the Middle 
Term is, by its position, the first; to us, on the contrary, 
it is the last. In fact, in his reduction of the Second and 
Third Figures to the First, Aristotle seems to have had in 
view, not only the establishment of the dictum de omni et 
nullo as the universal principle of all Syllogistic reasoning, 
but the restoration of the Middle Term to its proper in- 
termediate position. He was evidently thinking most of 
reasoning in Intension, and his followers of what is more 
frequent in use, though not more natural, — reasoning in 
Extension. In the later form, if the Minor Premise is 
stated first, the Middle Term becomes intermediate in 
position, as in the Aristotelic fonnula. 

In this exposition of Aristotle's mode of enouncement, 
as contrasted with that of the later logicians, Hamilton has 
merely followed Barth^lemy St. Hilaire ; in what follows, 
he is more original. 

" When logicians," he says, " came to enounce propo- 
sitions and Syllogisms in common language, the Subject 
being usually first, they had one or ottier of two difficulties 



THE HAMILTONIAN ANALYSIS. 241 

to encounter, and submit they must to either ; for they 
must either displace the Middle Term from its interme- 
diate position in the First Figure, to say nothing of revers- 
ing its order in the Second and Third ; or, if they kept it 
in an intermediate position in the First Figure (in the 
Second and Third, the Aristotelic order could not be kept), 
it behooved them to enounce the INIinor Premise first." 
Most of the older logicians adopted the latter alternative, 
stating the Minor Premise first in all the Figures ; and 
this seems the more natural order, if the Syllogism is used 
for the purpose of investigation and discovery. At a later 
period, when instruction, disputation, and proof came to 
be the chief purposes for which Syllogisms were formally 
enounced, the former alternative was adopted, and the 
Middle Term lost its proper intermediate position, the 
Major Premise being placed first in all the Figures. 

In the First Fignire, according to any mode of enounce- 
ment, the Middle Term must be the Subject of one of the 
Extremes (the two Terms of the Conclusion), and the 
Predicate of the other. Hence, in this Figure, there is a 
determinate Major and Minor Premise for reasoning in 
either Quantity, and but one direct or proximate Conclu- 
sion. If, in the Major Premise, the Middle Term is Predi- 
cate to the Subject of the Conclusion, then, in each of the 
three Judgments, the Subject includes the Predicate, and the 
reasoning is in the Quantity of Intension. If, on the con- 
trary, in the Major Premise, the Middle Term is Subject to 
the Predicate of the Conclusion, then, in each of the three 
Judgments, the Predicate includes the Sulrject, and the reason- 
ing is in the Quantitt/ of Extension. The relative position 
of the two Premises is really unimportant as respects the 
nature of the reasoning ; this depends upon the nature of 
the Middle Term, as including, or included under, the Sub- 
ject of the Conclusion. But following the established 
order of logical Quantity, that the greater should be placed 

11 F 



242 MEDIATE INFERENCE OR SYLLOGISM. 

first, the Middle Term as Subject, and the Predicate of 
the Conclusion as Predicate, should be the first or Major 
Premise for reasoning in Extension ; and the Middle Term 
as Predicate, with the Subject of the Conclusion as Sub- 
ject, should be the first or Major Premise in Intension. 
Thus : — 

In Extmdm. In Intension, 

M is P ; S is M ; 

S is M ; M is P ; 

.*. S is [included under] P. .'. S is [includes] P. 

Here, the relation of the Terms to each other in the 
Premises determines their relation to each other in the Con- 
clusion. If, in the Premises, M is included under P, and 
S included under M, then, in the Conclusion, S must be 
included under P. But if, in the Premises, S includes M, 
and M includes P, then, in the Conclusion, S must include 
P. Hence, in the First Figure, there can be but one 
direct Conclusion. 

In the two other Figures, it is not so; The Middle 
Term is not Subject of one and Predicate of the other Ex- 
treme, but is either, as in the Second Figure, Predicate of 
both, or, as in the Third, Subject of both. Consequently, 
in each of these Figures, the Middle Term either includes 
both the Extremes, or is included under both. As there 
is nothing, then, to determine the relative Quantity of the 
two Extremes to each other, either may be considered as 
Major in the Conclusion ; — we may conclude either that 
S is P, or that P is S. 

Though the First Figure has but one direct or immediate 
Conclusion, we may, by the medium of Conversion, obtain 
from it another Conclusion, which is then properly called 
indirect or mediate. Thus, in the formulas just given, hav- 
ing concluded directly that All S is P, we may then con- 
clude indirectly, or mediately, that Some P is S. But in 



TUE HAMILTONIAN ANALYSIS. 243 

the other Figures, there are two indifferent Conclusions, 
neither of which is more direct or immediate than the 
others. If A is B and C is B, we may conclude, with 
equal propriety and directness, either that A is C, or 
C is A; for there is nothing in the Premises to indicate 
whether A mcludes, or is included under, C. And in like 
manner in the Third Figure ; if B is A and B is C, the 
two Conclusions, A is C and C is A, are equally compe- 
tent and equally immediate. Of course, what has been 
called the Fourth Figure is merely the First, with its indi- 
rect Conclusion enounced as if it were direct or imme- 
diate ; it is a hybrid reasoning, with its two Premises in 
one Quantity, and its Conclusion in the other. Hence 
the Fourth Figure is properly abolished. 

In fact, all difference of Figure is unessential, — a mere 
accident of form. As it is demonstrated in the Hamil- 
tonian analysis, that a Judgment is a mere equation of its 
two Terms, it makes no difference which is stated first, — 
which is Subject or which is Predicate ; A = B and B = A 
are the same equation. Quantify the Predicate through- 
out, and this becomes evident. As all Conversion is then 
reduced to Simple Conversion, we have only to convert 
simply (retaining the subordination of the Terms) the 
Major Premise of the First Figiu'e in Extension, in order 
to produce the Second Figure ; convert its Minor Premise, 
and we have the Third. In Intension, this is merely re- 
versed ; convert the Minor for the Second, and the Major 
for the Third. 

To make the Syllogistic process depend upon the mere 
position, either of the two Terms as Subject or Predicate, 
or of the two Premises as enounced first or second, or of 
the Conclusion as expressed first or last, is to reduce Rea- 
soning to a mere accident of expression, and cause it to 
vary with the genius of different languages, or even with 
the mental peculiarities of individuals. Reasoning is a 



244 MEDIATE INFERENCE OR SYLLOGISM. 

process of Thought, not of language. It depends solely 
upon the relations of inclusion and exclusion, of subor- 
dination and superordination, of Intension and Exten- 
sion, existing between two Concepts and a Third ; and it 
must be regulated by universal laws, irrespective of differ- 
ences of language and peculiarities of mental habit. The 
order of enouncement is a convenient, though conven- 
tional, mode of indicating these relations to other persons, 
and even a safeguard against confusion and error in the 
successive elaboration of them in our own minds. But the 
actual inference, the mental process as such, is entirely 
independent of this order. 

To show further the unessential character of variation by- 
Figure, Hamilton pointed out the manner of abolishing the 
distmction of Subject and Predicate, and thereby reducing 
all Mediate Inference to what he calls the Unfigured Syl- 
logism. Any Syllogisms whatever may find adequate, 
though awkward, expression under this form. The two fol- 
lowing instances will suffice. 

Fig. I. Darii, reduced to an Unfigured Syllogism. 

All patriots are brave ; All patriots and some brave men 

are equal ; 
Some persecuted men are Some persecuted and some pa- 
patriots ; triots are equal ; 
.*. Some persecuted men are .•. Some persecuted and some brave 
brave. men are equal. 

Fig. n. Camestres. 

All animals are sentient ; All animals and some sentient 

things are equal ; 
Nothing unorganized is Any unorganized and any sen- 
sentient ; tient are not equal ; 
••.Nothing unorganized is •••Any unorganized and any an- 
animaL imal are not equaL 

In this Unfigured Syllogism, as Hamilton remarks, " the 



THE HAMILTONIAN ANALYSIS. 245 

dependency of Extension and Intension does not subsist, 
and accordingl}' the order of the Premises is wholly ai'bi- 
trary. This form has been overlooked by the logicians, 
though equally worthy of development as any other ; in 
fact, it affords a key to the whole mystery of Syllogism. 
And what is curious, the Canon by which this Syllogism is 
regulated (what may be called that of logical Analogy or 
Proportion) has, for above five centuries, been commonly 
stated as the one principle of reasoning, whilst the form of 
reasoning itself, to which it properly applies, has never been 
generalized. This Canon, which has been often errone- 
ously, and never adequately enounced, in rules four, three, 
two, or one, is as follows : — In as far as two notions 
(notions proper or individuals^ either both agree, or one 
agreeing the other does not, with a common third notion; in 
so far these notions do or do not agree with each other. This 
Canon thus excludes, — 1. an undistributed Middle Tenn, 
as then no common notion ; — 2. two negative Premises, 
as then no agreement of either of the other notions there- 
with." 

A convenient, though somewhat mechanical, rule for 
drawmg the correct Conclusion from any pair of Premises 
is the following, which was first stated by Ploucquet, and 
after him by Mr. De Morgan. Erase the symbols of the 
Middle Term, the remaining symbols show the inference. 
Deleatur in prcemissis medius ; id quod restat indicat conclu- 
sionem. Thus, in the two Syllogisms just given and re- 
duced to the Unfigured form, strike out from the Prem- 
ises, what I have italicized, all that relates to the Middle 
Term, and what remains of the Premises is the Conclu- 
sion. But it should be mentioned that this Rule, though 
valid for all the Aristotelic moods, does not hold good, as 
we shall see, for all the moods recognized under the Ham- 
iltonian system. 

Perhaps the most striking, and certainly the most con- 



246 JIEDIATE INFERENCE OR SYLLOGISM. 

venlent, improvement which Sir William Hamilton has 
made upon the labors of former logicians, is his system of 
notation, — a masterpiece of ingenuity in symbolization as 
respects perspicuity, completeness, and simplicity. It is 
valid for any system, and it manifests, at once, nearly all 
the alterations and improvements which he has made in 
the Aristotelic doctrine. It shows at a glance the equiv- 
alent Syllogisms in the different Figures, the convertible 
Syllogisms in the same Figure, and points out the two 
meanings which can be given to every Syllogism as inter- 
preted according to its Extension or its Intension, in refer- 
ence to the logical or the metaphysical whole. Even as a 
mnemonic contrivance, it is second in ingenuity and useful- 
ness only to the famous quatrain of hexameters, which 
contains the whole doctrine of the Reduction of the Moods 
of the lower Figures to the first Figure. 

The purpose of any system of notation is to manifest, by 
the differences and relations of geometrical quantities (lines 
or figures), the differences and relations of logical forms. 

A Proposition or Judgment is here indicated by a straight 
horizontal line, its two Terms or Extremes being placed at 
the extremities of that line, and represented, as usual, by 
letters. 

If, as in the Unfigured Syllogism, there is no distinction 
of Subject and Predicate, this line is made of equal thick- 
ness throughout. But if this distinction is introduced, 
then, as it is possible to read the Judgment in two ways, 
according to the Extension or the Intension of its Terms, 
(the Subject, in the latter case, including the Predicate, 
and in the fonner, being included under it,) the line is 
made wedge-shaped. Its broad end then represents the 
Subject of Extension or Breadth, and the thin end, that of 
Intension or Depth. A line gradually diminishing or in- 
creasing from end to end aptly indicates the relation be- 
tween two Quantities which are always co-existent, and in 



THE HAMILTONIAN ANALYSIS. 247 

inverse ratio to each other. As the employment of letters 
following upon each other in the same alphabet might sug- 
gest that one was invax'iably subordinated to the other, 
instead of being its subordinate in one Quantity and its 
superorduiate in the other, Hamilton uses for the Extremes 
the Latin C and Greek F, each being the third letter in 
its own alphabet ; as usual, M stands for the Middle Term. 
Thus : — 

is read, G and V are equal. 

may be read in two ways ; Extensively, O is included 
under F; Intensively, V is included in O: — or, in the 
usual manner, O is F, and F is (7, merely remembering, 
vrithout saying so, that Extension is signified in the former 
case, and Intension in the latter. 

Negation is indicated by a perpendicular stroke drawn 
through the line, thus : ^ — . The line without this stroke 
may be regarded as the Affirmative Copula ; with the 
stroke, as the Negative Copula. A colon (:) annexed to a 
Term shows that it is distributed, or taken universally ; a 
comma (,) so annexed, that it is undistributed or Particu- 
lar. When a Middle Term has a colon on the right, and a 
comma on the left, it is understood that it is distributed 
when coupled in a Judgment with the Term on the right, 
and undistributed when coupled with the other. 

A line drawn beneath or above three Terms indicates 
the Conclusion (or the Copula of the Conclusion) deduced 
from the two Premises which those Terms constitute. In 
the Second and Third Figures, since there may be two 
equally direct or immediate Conclusions, they are repre- 
sented by two such lines, the one above, and the other 
below the Premises. Thus : — 

1^ — — This is a Syllogism in the Second 

C, ^' , M : '■, F Figure, which may be read in 

i^^-^MHMi either of the following ways. 



248 MEDIATE INFERENCE OR SYLLOGISM. 

Extensively. Intensivel}/. 

Some C is some M ; All M is some T ; 

Some r is all M ; Some M is some C ; 

.'. Some r is some C ; or .-. Some C is some T ; or 

.-. Some C is some F. ,-. Some F is some C. 

P -, ^ T . I ,„ . p This is a Negative Syllogism in 

the First Figure, which may be 
read in either of the following 
ways ; but in either way, it has only one direct or imme- 
diate Conclusion, though a Second Conclusion may be ob- 
tained from it indirectly^ by converting simply the proper 
or dii'ect Conclusion. 

Extensively. Intensively. 

Some M is some C ; No M is any F ; 

No F is any M ; Some C is some M ; 

No F is some C ; or, Some C is not any F ; or, 

indirectly, indirectly. 

Some C is not any F. Not any F is some C. 

The following diagram presents the whole Hamiltonian 
doctrine of Figure, together wdth the distinction between 
the Analytic and the Synthetic order of enouncement. 
After the explanations which have been given, it will be 
easily understood. 

As a Judgment has been designated by a line, a Syllo- 
gism, which is a union of three Judgments, is appropriately 
typified by a triangle, a union of three lines, of which the 
base repi'esents the Conclusion, and the other tAvo lines, 
the Premises. As the direction of the arrows indicates, 
we may proceed either in the usual or Synthetic order, 
from the Premises to the Conclusion, or in tlie reverse 
order, which is Analytic, from the Conclusion to the Prem- 
ises. As there is no valid reason for always placing the 
Major Premise first in order, the diagram shows that either 
Premise may have precedence in this respect, so that what 
has been called the Fourth Figure is here identified with 
the Indirect Moods of the First. 



THE HAMILTONIAN ANALYSIS, 



249 




5K 5K ^ 



The Unfigured Syllogism is properly represented as in- 
cluding all the others, as any Syllogism of either Figure 
may be easily expressed in this form. In like manner, the 
triangle representing the First Figure is made to include 
the two typifying respectively the Second and Third, as 
either of the latter may be readily reduced to the former. 
And again, the essential unity of the Syllogistic process, 
and the miessential nature of variation by Figure, are ap- 
propriately signified by a single triangle comprehending all 
the varieties of form. 

" The double Conclusions, both equally direct, in the 
Second and Third Figures, are shown in the crossing of 
two counter and corresponding lines. The Direct and 
Indirect Conclusions in the First Figure are distinctly 
typified by a common and by a broken line ; the broken 
line is placed immediately under the other, and may thus 
indicate that it represents only a reflex of — a consequence 
11* 



250 MEDIATE INFERENCE OR SYLLOGISM. 

through — the other (^Kar dvuKXaa-tv, refleadm, per re- 
Jtexionern). The diagram therefore can show, that the 
Indirect Moods of the First Figure, as well as all the Moods 
of the Fourth, ought to be reduced to merely mediate in- 
ferences ; — that is, to Conclusions from Conclusions of the 
conjugations or Premises of the First Figure." 

If we have the two Premises, All C is some M, and All 
Mis some T, and consider that some Jf is a Mark of (or, 
is included in) all C, and some F a Mark of all M, then 
we are reasoning in the Quantity of Intension ; and, accord- 
ing to the Axiom that a Mark of a Mark is also a Mark of 
the thing itself the proper and direct Conclusion is. All C is 
some r. But if we conclude that Some T is all (7, accord- 
ing to the Fourth Figure or the Indirect Moods of the 
First, Some T does not appear as a Mark of all (7, but as 
included under it, — as a Subject of Extension ; the Prem- 
ises, then, would be represented in one Quantity, and the 
Conclusion in the other. " But though always coexistent, 
and consequently always, to some amount, potentially in- 
ferring each other, still we cannot, without the interven- 
tion of an actual inference, at once jump from the one 
Quantity to the other, — change, per saltum. Predicate 
into Subject and Subject into Predicate. We must pro- 
ceed gradatim. We cannot arbitrarily commute the 
Quantities, in passing from the Qusesitum to the Prem- 
ises, or in our transition from the Premises to the Con- 
clusion. When this is apparently done, the procedure is 
not only unnatural, but virtually complex and mediate, 
the mediaey being concealed hy the concealment of the mental 
inference which really precedes " ; — indicated by the broken 
line in the diagram. 

One other species of Hamiltonian notation should be 
noticed, as it brings to light very clearly the virtual equiva- 
lence of those Moods in the several Figures which are in- 
dicated, in the old mnemonic hexameters, by names begin- 



THE HAMILTONIAN ANALYSIS. 251 

ning with the same capital letter. Four straight lines are 
all that is needed for such a notation. Three of these are 
horizontal, to represent the Terms ; and one perpendicular, 
or the want of it, at the beginning of the comparison, to 
express the Quality of Affirmation or Negation. " Quan- 
tity is marked by the relative length of a terminal line 
within, or its indefinite excursion before, the limit of com- 
parison. This notation can represent equally total and 
ultratotal distribution, in simple Syllogism and in Sorites ; 
and it shows at a glance the competence or incompetence 
of any Conclusion." 



" Of these, the former, with its converse, includes Darii, 
Dabitis, Datisi, Disamis, Dimaris, &c. ; whilst the latter, 
with its converse, includes Celarent, Cesare, Celanes, Ca- 
mestres, Cameles, &c. But of these, those which are rep- 
resented by the same diagram are, though in different 
Figures, formally the same Mood." " In aU the other 
geometrical schemes hitherto proposed, whether by lines, 
angles, triangles, squares, or circles, the same complex 
diagram is necessarily employed to represent an indefinite 
plurality of Moods." 

The application of Hamilton's doctrine of the thorough- 
going quantification of the Predicate to the explication of 
the Syllogistic theory produces, as might have been ex- 
pected, a great enlargement of the number of Moods. If 
there are hut four fundamental Judgments, the number of 
conceivable Moods that can be framed from them, by taking 
them three and three, is sixty-four * ; excluding fi'om these 

* The computation is easily made. The four letters A, E, I, O, give 
us four different Major Premises ; each of these may have four different 
Minor Premises ; — hence there will be sixteen pairs of Premises. But 
each of tliese pairs may be conceived to have four different Conclusions : 
whence, 16 X 4 = 64 conceivable Moods. 



252 MEDIATE INFERENCli OR SYLLOGISM. 

the invalid Moods, as offending against one or more of 
the general Rules of the Syllogistic process, there remain 
only fourteen as valid in some one of the first three Fig- 
ures ; — nineteen, if we admit the Fourth Figure ; — twenty- 
four, if we include also the anonymous indirect Moods. 
But under the Hamiltonian doctrine of eight fundamental 
Judgments, we have five hundred and twelve * conceivable 
Moods. Excluding from these all that offend against the 
General Canon, (as by having an undistributed Middle, 
two Negative Premises, or collecting more in the Conclu- 
sion than was distributed in the Premises,) there remain 
thirty-six valid Moods, of which twelve are Affirmative and 
twenty four Negative. On this doctrine, each Affirmative 
Mood yields two Negative ones, as each of its Premises 
may be successively negatived. Figure now appears in its 
true character, as an unessential variation ; but as each of 
these valid Moods can, if we please, be thrown into either 
of the three Figures, there are 36 X 3 = 108 vahd Moods, 
reckoning as such all the modifications of statement of 
which they are susceptible. But to show how trifling are 
the changes thus effected by carrying what is really one 
Mood through each of the three Figiu'es, I borrow a con- 
crete example from Mr. Baynes. 

Fig. L Fig. II. 

All man is some animal ; Some animal is all man ; 

Every Celt is some man ; Every Celt is some man ; 

.*. Every Celt is some animal. .•. Every Celt is some animal. 

Fig. in. 

All man is some animal ; 

Some man is every Celt ; 

.•. Every Celt is some animal. 

* Computing as before, from eight Judgments we hate eight different 
Major Premises, each of which may have eight different Minor Premises, 
whence 8 X ^ = 64 pairs of Premises ; and as each of these may have 
eight different Conclusions, there are 64 X ^ ^ 512 triplets of Judgments, 
or conceivable Syllogisms. 



THE HAMILTONIAN ANALYSIS. 253 

Hamilton's General Canon has already been enounced 
in the mode of statement in which it is directly applicable 
to the Unfigured Syllogism. As applied to tlie Figured 
Syllogism, wherein we have to consider the two counter 
Quantities of Extension and Intension, it should be thus 
expressed: — " What worse relation of Subject and Predi- 
cate subsists between either of two Terms and a common 
Third Term, with which one at least is positively [affirma- 
tively] related, that relation subsists between the two 
Terms themselves." As already stated, this Canon is 
only a succinct statement of the six general Rules which 
have been laid down as fulfilled in every valid case of 
Mediate Inference ; and it is, also, only a restatement of 
the two Primary Axioms of Pure Thought, the laws of 
Identity and Non-Contradiction, with the necessary con- 
ditions and limitations which determine their application. 
As these Rules and Axioms were found to hold good under 
the Aristotelic doctrine of four fundamental Judgments, 
they are also valid under the system which increases the 
number of these Judgments to eight. No Syllogism can 
be invalid which accords throughout with this Canon, and 
every illegitimate process, either directly or indirectly, 
openly or covertly, violates it. 

But we must accurately determine which is the " worse 
relation " of Subject and Predicate that can subsist be- 
tween either of two Terms and a common Third Term. 
When there are but four Judgments, the corresponding 
principle, that the Conclusion follows the " weaker part," 
admits of easy interpretation ; Particular Quantity is 
weaker than Universal, Negative Quality is weaker than 
Affirmation. But with eight Judgments, the various de- 
grees of better or worse, stronger or weaker, must be 
more precisely ascertained. Always considering Negation 
as weaker than Affirmation, we now say that the best 
(strongest) Quantity of Affirmation is the worst (weakest) 



254 MEDIATE INFERENCE OH SYLLOGISM. 

Quantity of Negation. In other words, we affirm heat when 
we affirm all, and affirm worst when we affirm only some ; on 
the contrary, we deny best when we deny only some, and 
deny worst when we deny all. On account of this inverse 
relation of the two Quantities, an Affirmative Mood with a 
Particular Conclusion may be changed, by merely nega- 
tiving one of its Premises, into a Negative Mood with a 
Universal Conclusion. But though the Quantity is thus 
altered from Particular to Universal, this is not a change 
from worse to better, but from worst to worst ; for though 
a Particular stands lowest in the scale of Affirmation, a 
Universal stands lowest in the scale of Negation. The 
seeming exception only confirms the rule, and proves that 
the Canon is universally appHcable. Take the following 
instance : — 

C : -, M : : T Some M is all C ; 

■ , All r is all M ; 

.-. Some r is all C. 
Some blacks are all slaves ; 
All of African descent are all blacks ; 
.'. Some of African descent are all slaves. 

Now, if we negative this Syllogism by negativing the 
Minor Premise, the Conclusion changes from Particular to 
Universal, thus : — 

p Some M is all C ; 
No r is any M ; 
■ No r is any C. 

Some blacks are all slaves ; 
No Caucasian is any black ; 
.*. No Caucasian is any slave. 

This change, though from Particular to Universal, is 
really from the worst of Affirmation to the worst of Nega- 
tion. But such changes are infrequent, as, in the inter- 



THE HAMILTONIAN ANALYSIS. 



255 



mediate relations, the commutation is only from equal to 
equal, and the predesignations of Quantity, in their in- 
verse signification, remain externally the same. Out of 
the twenty-four valid Negative Moods, only four cases are 
found of a Particular quantification disappearing in the 
Negative Conclusion. Hamilton gives the following ar- 
rangement of the eight Judgments in the order proceeding 
from best to worst. 

Best. 



-1. 


Afa. 


All are all. 


-2. 


Afi. 


All are some. 


-3. 


Ifa. 


Some are all. 


4. 


Ifi. 


Some are some. 


■5. 


Ini. 


Some are not some 


•6. 


Ina. 


Some are not any. 


•7. 


Ani. 


Not any is some. 


8. 


Ana. 


Not any is any. 



Wont, 

With these explanations, the following list of the twelve 
valid Affirmative Moods in each of the three Figures, and 
the 24 valid Negative Moods in the First Figure, all ex- 
pressed in the Hamiltonian notation, will be found intel- 
ligible. 

In this Table, the Quantity of the Conclusion is marked 
only in the cases already considered, wherein the Terms 
obtain a different Quantity from that which they held in 
the Premises ; accordingly, when not marked, the quanti- 
fication of the Premises is held as repeated in the Conclu- 
sion. The symbol — — ^ placed beneath a Conclusion, 
indicates that, when the Premises are converted, the Syllo- 
gism remains in the same Mood ; )><^ shows that the two 
Moods between which it stands are convertible into each 
other by converting their Premises. The Middle Term is 
said to be balanced, when it is Universal in both Premises. 
The Extremes, or Terms of the Conclusion, are balanced, 
when both alike are distributed ; unbalanced, when one is, 
and the other is not, distributed. Accordingly, of the 



256 



MEDIATE INFERENCE OR SYLLOGISM. 



B 



L C:- 

ii. C ,- 

iii. C,- 

iv. C:- 

■ V. C- 

vL C- 

vii. C :- 



viii. C ,- 
ix. C:- 



X. C:- 



XI. c :- 



xii. C- 



SCHEME OF NOTATION- 
TABLE OF SYLLO- 

A. AFFIRMATITE MOODS. 

Fig- I. Fig. ii. 



M 



M 



:M, 



X 

i,M: . 



M 



X 



M 



>< 

I : M : - 



M 



>< 

I ,M: - 



:M, 



X 

I , M: 



■, r 



■,r 

■:r 
i:r 



■,r 



i.r 



:M 



C,i 



:M: 



■,r 



C,i 



M 



•, r C :, 




X 



C:i 
I 



, M 



M 






X 



: M 



: M , 



X 



,M: 



M 



■,r 



X 



C,i 



, M: 



NoTK. — A. 1. and ii. are Balanced. B. The other moods are Unbalanced. Of these, 



THE HAMILTONIAN ANALYSIS. 



257 



FIGURED SYLLOGISM. 
GISTIC MOODS. 

A. AFFIRMATrVE MOODS. 
Fig. III. 



C,- 

c,- 

C:- 
C,- 

C,- 
C:- 

C,- 

C:- 
>~ 

C:- 



]M : 



: M, 



X 



,M 



:M 



-,r 

I 

-T 

-,r 
-,r 



X 



M : 



-,r 



X 



: M 



-:r 



M , 



X 



, M 



>BI 



M, 



-.V 



-,r 



X 



c,- 



M 



B. NEQATIVE MOODS. 
Fig. I. 
M 




iii. and iv. are unbalanced in terms only, not in propositions ; the rest in both. 



258 MEDIATE INFERENCE OR SYLLOGISM. 

Moods in the Table, numbers I. and II. are balanced as 
respects both Terms and Propositions ; in III. and IV., 
only the Terms are unbalanced; in the remainder, both 
Terms and Propositions are unbalanced. 

" If we apply the Moods to any Matter^ however ab- 
stract, say letters, there will emerge forty-two Syllogisms ; 
for the formal identity of the balanced Moods will then be 
distinguished by a material difference." Thus, numbers I. 
and II., with the four Negative Moods formed from them 
by successively negativing each of their Premises, will, 
when thus treated, yield six additional Syllogisms, making 
forty-two in all. Take for instance, number. I., Affirma- 
tive ; when each of its Judgments is converted, it is still 
in the same Mood. 

Converting each Judgment. 
I. All rational are all risible ; All risible are all rational ; 

All men are all rational ; All rational are all men ; 

.". All men are all risible. .•. All risible are all men. 

" On the contrary, if we regard the mere formal equiv- 
alence of the Moods, these will be reduced to twenty-one 
reasonings, — seven Affirmative and fourteen Negative." 
For, of the unbalanced Moods, every odd number is con- 
verted into the even number immediately following; and 
thus, if each Mood is regarded as formally equivalent to its 
converse, (and numbers I. and II. are so regarded in the 
Table,) numbers IV., VI., VIII, X., and XII. must be 
struck out of the enumeration, and only seven valid Af- 
firmative Moods remain. In like manner, in Negatives, 
the first and second Moods (a, U) of the pair correspond- 
ing to the even number which was struck out, are reduced 
from or to the second and first Moods (6, a) of the odd 
number which was retained. Five pairs being thus elim- 
inated, only seven pairs — fourteen valid Negative moods 
— remain. 

Under the Aristotelic doctrine, as we have seen, logi- 



THE HAMILTONIAN ANALYSIS. 259 

clans found that the six general Rules, which they had 
enounced as governing all Mediate Inference, did not suf- 
fice to determine which of the Moods were valid, and 
vfhich \nvalid, in each of the four Figures. The variations 
of Fig^ire depend upon the relative position of the Middle 
Terv •• as Subject or Predicate to each of the two Terms 
of the Jonclusion ; and special Rules were necessary to 
prevent ihese variations from conflicting with the two 
principles ^'nch, according to the Aristotelians, determine 
the implicit quantification of the Predicate. These prin- 
ciples are,— I. That in all Affirmative Judgments the 
Predicate is Particular ; and, 2. That in all Negative Judg- 
ments the Pred ^^ie is Universal. Now, in the Second 
Figure, the Middk Term being Predicate in both Prem- 
ises, the logicians we^ > compelled, in order to prevent the 
infringement of the Gfe ex-al Rule, that the Middle Term 
must he distributed in at k st one of the Premises, to enact 
the Special Rule, that, in th. 's Figure, one of the Premises, 
and consequently the Conclusi^ h acso, must he Negative. 
But under the Hamiltonian sysv ^m of the thorough-going 
quantification of the Predicate, sin m the Middle Term can 
be distributed when it is the Predivrnte of an Affirmative, 
just as well as when it is the Prt licate of a Negative 
Judgment, this Special Rule is bo i useless and false. 
And so with all the other Special R les for each of the 
Figures. They are needless, because they were formed 
only on the supposition that the Pre(*icate could be but 
partially quantified ; they are false, bee mse the thorough- 
going quantification of the Predicate brings to light many 
valid forms of Syllogism which violate • ach of these rules. 

The following demonstration of the i^lsity of these Spe- 
cial Rules is borrowed in part from \ Iv. Baynes's " New 
Analytic of Logical Forms." 

The Rules of the First Figure are,- t. That the Sump- 
tion must be Universal; 2. That th** Subsumption must 



260 MEDIATE INFERENCE OR SYLLOGISM. 

be Affirmative. Quantify the Predicate, and neither of 
these holds good. 

First Rule falsified. 

Some men are some fleet-footed ; 

All rational is all man ; 
.*. Some rational is some fleet-footed. 
Second Rule falsified. 

All idealists are some philosophers ; 

No sensualist is any idealist ; 
.*. No sensualist is some philosopher. 

The Rules of the Second Figure are, — 1. That one of 
the Premises must be Negative ; 2. That the Sumption 
must be Universal. Both are abrogated by a quantified 

Predicate, thus : — 

First Rule falsified. 

All risible is all man ; 
All philosophers are some men ; 
.*. All philosophers are some risible. 

Second Rule falsijied. 

Some mortal is all man ; 
All rational is all man ; 
.*. All rational is some mortal. 

The Rules of the Third Figure are, — 1. That the Sub- 
sumption must be Affirmative ; 2. That the Conclusion 

must be Particular. 

First Rule falsijied. 

All fi:ee agents are all responsible ; 
No free agent is any brute ; 
.*. No brute is any responsible. 

Second Rule falsified. 

All triangles are halves of parallelograms ; 
All triangles are all trilaterals ; 
.'. All trilaterals are halves of parallelograms. 

All the Special Rules being thus abrogated, the unity 



THE HAMILTONIAN ANALYSIS. 261 

and simplicity of the Syllogistic process become manifest. 
Hamilton's Supreme Canon, which is a mere compend of 
the six General Rules, appears as the universal and all- 
sufficient law of Mediate Inference, and the science of 
Logic is freed from the encumbrance of a mass of needless 
distinctions and superfluous details. As Figure is demon- 
strated to be an unessential variation, all the Rules for 
Reduction are swept away. In fact, the process of Reduc- 
tion is so far simplified by allowing all Judgments to be 
converted simply, that, if we still need to have recom-se to 
it in order that the reasoning may appear in its most ob- 
vious and natural form, the requisite changes suggest them- 
selves, and the work may be performed without the aid of 
rules. 

Some observations are necessary, however, in respect to 
the applicability of the different Figures to those two di- 
rections of the reasoning process which are called Deduc- 
tive and Inductive. This subject has been so well ex- 
plained by Mr. Baynes, that I borrow his language. We 
have seen that the characteristic of reasoning in Intension 
— or Comprehension^ as it is more fi'equently called — is, 
that the Predicate is contained in the Subject ; of reason- 
ing in Extension, that the Subject is contained under the 
Predicate. " This being remembered," says Mr. Baynes, 
" it will appear that in the Second Figure, where the Mid- 
dle Term as Predicate contains both the Subjects under it^ 
Extension will predominate. In the Thu'd, where the Mid- 
dle Term as Subject is contained under, and therefore com- 
prehends in it both the Predicates, Comprehension will pre- 
vail. In the First Figure, again, where the Middle Terra 
is both Subject and Predicate, Extension and Comprehen- 
sion balance each other. The First Figure is indifi:erently 
competent to either. 

" Reasoning, however, proceeds not only in diflforent 
wholes, but in different aspects of the same whole. We 



262 MEDIATE INFERENCE OR SYLLOGISM. 

may, it is evident, regard any whole, considered as the 
complement of its parts, in either of two ways ; for we 
may, on the one hand, look from the whole to the parts, 
and reason accordingly downwards; or, on the other 
hand, look from the parts to the whole they constitute, 
and reason accordingly upwards. The former of these 
•easonings is called Deductive, the latter Inductive. De- 
j^uctive reasoning is founded on the maxim, ' What be- 
longs to the containing whole belongs also to the con- 
tained parts ' ; Induction, on the contrary maxim, ' What 
belongs to the constituent parts belongs also to the con- 
stituted whole.' Thus, in Deductive reasoning, the whole 
is stated first, and what is affirmed of it is affirmed of the 
parts it contains ; in other words, a general law is laid 
down, and predicated of the particular instances to which 
it applies. In Inductive reasoning, the parts are first stated, 
and what is predicated of them is also predicated of the 
whole they constitute ; in other words, the particular in- 
stances are first stated as facts, and then the law they con- 
stitute is evolved. 

" This being the nature of these counter and correlative 
reasonings, it appears to us, that, though each kind is com- 
petent in either whole (Extension or Comprehension), yet 
the reasoning in the whole of Extension is more naturally 
allied to the Deductive, and that in Comprehension to the 
Inductive. For, in the whole of Extension, the reason- 
ing proceeds from the general to the special, — from the 
abstract to the concrete, — from general laws to the par- 
ticular instances which are contained under them ; while 
in that of Comprehension, on the other hand, the reasoning 
proceeds from the special to the general, — from the con- 
crete to the abstract, — fi'om the particular instances to the 
general laws, whose operation they exemplify. 

" Considering these kinds of reasoning in relation to the 
Figures, it will appear, then, that since Extension prevails 



THE HAMILTONIAN ANALYSIS. 263 

in the Second, that will be so far more suitable for Deduc- 
tive reasoning; and since Comprehension prevails in the 
Third, that Figure will so far be more adapted for Induc- 
tive reasoning ; Avliile, since Extension and Comprehension 
prevail equally in the First, that Figure will be equally- 
fitted for either kind of reasoning. 

" The relation of the Figures to these different kinds of 
reasoning will be best illustrated by an example. We will 
take first the Second Figure : — 

Fig. II. 
Deductive Reasoning : Quantity of Extension. 
Endowed mth reason is all man. 
European, Asiatic, African, American, are all man. 
European, Asiatic, African, American, are endowed with reason. 

" Here the reasoning is Deductive, for the law is first 
enounced, the individual instances are next brought under 
it, and it is then affirmed of them ; it is Extensive, for it 
proceeds fi'om the wider notion through the narrower to 
the individual. Let us noAv take the same Terms and treat 
them Inductively, beginning with the individuals. The 
reasoning will then be in the whole of Comprehension, and 
will naturally appear in the form of the Third Figure : — 

Fig. III. 
Inductive Reasoning ; Quantity of Comprehension. 
European, Asiatic, African, American, are all man. 
European, Asiatic, African, American, are endowed with reason. 
Endowed with reason is all man. 

" Here the reasoning is Inductive, for, beginning vd\h the 
individuals in the Premises, we arrive at the law (with 
which we started in the previous Syllogism) in the Conclu- 
sion ; it is Comprehensive or Intensive, for it proceeds from 
the concrete to the abstract, from a greater totality of attri- 
bute to a less. In other words, in either Quantity (Exten- 
sive or Intensive), we reason from the greatest whole ; but 



264 MEDIATE INFERENCE OR SYLLOGISM. 

in the Quantity of Extension, the greatest whole is the most 
abstract notion (i. e. the widest law), whereas in that of 
Comprehension, the greatest whole is the most concrete 
notion (i. e. the individual instance). But proceeding 
thus from the widest law, the reasoning is necessarily 
Deductive, while on the other hand, proceeding from the 
individual instance, it is as necessarily Inductive. 

" We may give the same example in the First Figure, to 
illustrate (what will now be quite obvious) that it is in- 
differently competent to either reasoning : — 

Fig. L 
Deductive Reasoning : Quantity of Extension. 
All man is endowed with reason. 
European, Asiatic, African, American, are all man. 
European, Asiatic, African, American, are endowed with reason. 

Inductive Reasoning : Quantity of Comprehension. 
European, Asiatic, African, American, are all man. 
All man is endowed with reason. 
European, Asiatic, African, American, are endowed with reason. 

" The Second and Third Figures are indeed naturally 
respectively connected with Deductive and Inductive rea- 
soning ; for in the Second, we judge the likeness or unlike- 
ness of two parts, as they are contained or not contained by 
a common whole ; while in the Third, we judge the likeness 
or unlikeness of two wholes, as they severally contain oi 
do not contain common parts." 

In respect to Hypothetical and Disjunctive reasoning, 
Hamilton has followed Kant in declaring that all Mediate 
Inference is one, — that which has been denominated Cate- 
gorical ; all the so-called Conditional Syllogisms are reduci- 
ble to Immediate Inferences. Their characteristic feature 
is, that they have no Middle Term ; the agreement or dis- 
agreement of the two Terms of the Conclusion with each 
other is ascertained, not by comparing each of them sep- 
arately with a third Term, which is a mediate process, but 



THE HAMILTONIAN ANALYSIS. 265 

directly, from a single Premise, here incorrectly styled a 
Major Premise. This Premise consists, not of two Terms 
merely, but of tAvo Judgments, called respectively the Ante- 
cedent and the Consequent ; a relation of mutual depend- 
ence is affirmed to exist between these, by "vartue of which 
the Axiom of Reason and Consequent becomes applicable 
to the case. This Axiom, as has been shown (page .54), 
is directly explicated into the two Laws, — 1. That to affirm 
the Reason or the Condition is also to affirm the Consequent ; 
and, 2. That to deny the Consequent is also to deny the 
Reason. A ratione ad rationatum, a negatione rationati ad 
negationem rationis, valet consequentia. Tlie single Prem- 
ise affirming that this relation of Reason and Consequent 
exists between the Judgments Avhich are its two parts, this 
Axiom compels us to infer immediately, or without the aid 
of a third Term, both that the Consequent follows when 
the Antecedent is posited, and that the Antecedent is de- 
nied when the Consequent is sublated. 

The reduction of a Hypothetical Judgment to a Cate- 
gorical shows very clearly the Immediacy of the reasoning 
in what is called a Hypothetical Syllogism. Thus, If A is 
R, C is J), is equivalent to - 

All cases of A is B are cases of C is D. 
Some cases of A is B are cases of 



This case of A is B is a case of 
In such reasoning, as Kant remarks, the Premise does 
not affi)rd a proof of the Conclusion, but a ground or man- 
ner of proving it ; it is then only an explication of the 
meaning of the Premise, when we say that the Consequent 
holds good when the ground or Reason exists, and that the 
Reason does not exist if the Consequent does not hold 
good. Hence, this kind of reasoning may properly be 
referred to the doctrine of Exponibles. All the Matter 
which we are reasoning about is embraced in the one com- 
plex proposition that is here called the Premise ; and aU 

12 



266 MEDIATE INFERENCE OR SYLLOGISM. 

that the reasoner has to do is to explicate or interpret this 
proposition. Considered as an Exponible, the Conditional 
Judgment, If A is B, C is D, may be interpreted in two 
ways, — 1. as a Restrictive; 2. as an Exclusive. The 
first of these interpretations yields, by the Immediate In- 
ference of Subalternation, what is called the Modus ponens 
of Conditional Reasoning ; the second yields, also Imme- 
diately, the Modus tollens. 

1. Thus, Restrictively, in affirming that, if A is B, G is 
J>, we do not say, C is always D, but only, " All C, when 
A is B, is D," the italicized clause being the Restriction, 
and answering to a limiting adjective, — saj, yellow : All 
yellow C is B. Then, by Subalternation, 



Some yellow C ) • -p. 
This yellow C ) 



yelk 

Again, the same Judgment, If A is B, C is B, yields, by 
the Immediate Inference of Contraposition, If is not B^ 
A is not B. This is an Exclusive ; it affirms that 
A is B only when C is D ; then. Immediately, 
A is not B when C is not B. 
In fact, all reasoning is hypothetical ; the Syllogism, as 
such, does not affirm its Conclusion absolutely, but only its 
dependence on the Premises. If the Premises are true, 
tlie Conclusion follows. Any Immediate Inference, also, 
may be stated hypothetically. Take that by Subalterna- 
tion, for instance : — 

All A is B ; 
.*. Some A is B. 

Stated hypothetically thus : — 

If all A is B, some A is B ; 
.•. Some A, or this A, is B. 

It is unnecessary to consider separately the case of Dis- 
junctive reasoning ; for it has already been proved (page 
181) that Disjunctives are only complex Hypotheticals. 



OP FALLACIES. 267 



CHAPTER IX. 



OF FALLACIES. 



A FALLACY is any instance of unsound or invalid 
reasoning which has a deceptive appearance of cor- 
rectness and truth. If it be such that the writer or speaker 
is himself deceived by it, it is called a Paralogism ; if 
framed by him for the purpose of deceiving others, while 
he is himself aware of its unsoundness, it is a Sophism. 
Those of the former class are what we have most to dread ; 
for on account of the necessary dependence of Thought on 
Language, we often commit them in our silent meditations, 
while we are attempting to discover the truth or to dis- 
intricate it fi'om error. The danger is greatly enhanced 
by the symbolic or algebraic use of Language, whereby 
we employ words for the moment as mere signs, without 
spreading out their signification before the mind, and thus 
are often deceived by their ambiguity and vagueness. 
Sophisms are comparatively of rare occurrence, as one 
who wishes to deceive can do so more easily and effect- 
ually by false statements than by false reasonings. It is 
more difficult to weave invalid but specious arguments, 
knowing their incorrectness, than to reason correctly from 
wrong premises. Formerly it was otherwise ; the great 
use of disputation by the ancient sophists and the School- 
men, as a logical exercise and a means of education, tended 
to create a special art of sophistry, and has left on record a 
multitude of logical puzzles for the amusement of later 
times. Dexterity in framing and solving these sophisms 



268 OF FALLACIES. 

was reckoned a scholarly accomplishment, and one of the 
special fruits of a university education. Nowadays this 
species of mental gymnastics has fallen into entire disre- 
pute, as men prefer to sharpen their wits on graver matters 
and subjects of more immediate interest. 

The purpose of the doctrine of Fallacies, as it is now 
taught, is to familiarize the mind with those instances of 
erroneous reasoning which are most likely to lead our own 
thoughts astray in the search after truth and the elimina- 
tion of error. For this end, a classification of Fallacies is 
desirable. The earliest attempt, of which we have any 
distinct knowledge, thus to reduce them to system, was 
that of Aristotle ; and the chief endeavor of later logicians 
has been to ascertain, develop, and illustrate his meaning. 
Even the phraseology which he employed became conse- 
crated, as it were, by long use in the Schools ; and the 
chief dispute among modern writers has been, whether a 
particular Fallacy is rightly designated by this or that tech- 
nical name. A more unprofitable logomachy can hardly 
be imagined. Our business is to teach Logic, and not to 
write a commentary upon Aristotle. The classification 
framed by him, though a marvellous work for the time, 
evincing the prodigious acuteness and comprehensiveness 
of view for which his intellect was so remarkable, must 
still, if viewed under the lights of modern science, be re- 
garded as crude and imperfect. A better arrangement can 
be effected, not by laying aside liis phraseology altogether, 
but by employing his technical terms, when they are con- 
venient, under the conventional meaning which has long 
been assigned to them, and by striking out many of his dis- 
tinctions, and introducing others in their place Avhich have 
been suggested by later experience. The use of classifica- 
tion, it must be remembered, is merely subsidiary ; the 
main purpose is to become familiar with the character- 
istics of those forms of erroneous reasoning which most 



OF FALLACIES. 269 

frequently occur in practice ; and this can be best accom- 
plished by dividing them into species, and discriminating 
these species from each other. 

It should be observed that, strictly speaking, the consid- 
eration of Fallacies is extralogical. We have already laid 
down the Rules of correct or valid Inference ; any argu- 
mentation which violates one or more of these Rules is in- 
vahd. But an open violation of one of them, as, from its 
veiy obviousness, it is not likely to deceive anybody, is not 
usually called a Fallacy. A classification of what are prop- 
erly denominated Fallacies would depend on an enumera- 
tion of those circumstances which are most likely to deceive 
us — to cover up the violation of a Rule — in the forma- 
tion of our Judgments and Inferences ; and a disquisition 
on these circumstances would form a valuable chapter of 
Psychology, or in a Treatise on the practical Conduct of 
the Understandinor. The chief source of these errors is 
the ambiguity of language, both as respects the meaning 
of single words (cequivocatio^ and the construction of 
sentences (amphiholia). Then the ultimate remedy for 
them is to be found in the study of language ; it would be 
a part of the doctrine of Hermeneutics, or the science of 
Interpretation. But as certain prominent classes of them 
frequently perplex and vitiate our reasonings, a description 
of such is not entirely out of place as an appendage to the 
science of Logic. 

We observe in the first place, then, that Aristotle was 
wrong, and his authority has misled most of the later logi- 
cians, in forming a distinct class of the Fallacies of language. 
His first distinction is between those in diethne, which 
arise merely from the improper use of words as arbitrary 
signs of thought, and which, therefore, generally disappear 
when the proposition is translated into another language, 
and those extra dictionem^ which are in the Thought iteelf, 
whether in its Matter or its Form, and therefore adhere to 



270 OF FALLACIES. 

the Thouglit, however it may be expressed. He enumer- 
ates six classes or subdivisions of the former; but the 
division is a faulty one, as the six can be reduced to two, 
namely, the ambiguity of single words, or the ambiguous 
construction of sentences. But we object generally, that 
the erroneous use of language is of no logical import what- 
ever, if it be not employed to hide some defect in the rea- 
soning. The ambiguity of words may cloak, but does not 
constitute, the sophism. If the suspected Syllogism does 
not contain an undistributed Middle, or four Terms instead 
of three, or an Illicit Process, or some other violation of 
logical Rule, it is a sound Inference, however faulty may 
be the language in which it is expressed. Accordingly, it 
will b(\ found, that all the instances given in the books to 
illustrate the six classes of what may be briefly termed 
Verbal Fallacies, resolve themselves, when the ambiguity 
is detected, into logical quadrupeds, as Syllogisms with/^mr 
Terms have been derisively called, or some other form of 
violatino; one or more of the Canons of Pure Logic. Take 
the following illustration, from Mr. De Morgan, of the Fal- 
lacy of ambiguous words, Aristotle's first subdivision. 

All criminal actions ought to be punished by law ; 

Prosecutions foi* theft are criminal actions ; 

Therefore, prosecutions for theft ought to be punished by law. 
Here the Middle Term, criminal actions, is ambiguous ; in 
the Sumption, it means immoral deeds ; in the Subsump- 
tion, it is a technical phrase for a particular class of legal 
proceedings. Substitute these definitions for the phrase 
defined, and it is apparent that the pretended Syllogism is 
a quadruped. 

Take the followino; as an instance of Aristotle's second 
subdivision, — ambiguous construction. 

All that glitters is not gold ; 

Tinsel glitters ; 

Then, tinsel is not gold. 



OF FALLACIES. 271 

Here, in the Sumption, the Middle Tenn is apparently 
distributed by the predesignation all; but it is not so in 
reality, as the negative particle ought to be construed as 
qualifymg all, and not all means some are not. But if we 
read. Some things that glitter are not gold, the Middle is not 
distributed in either Premise. 

The class of Verbal Fallacies, then, should be abolished, 
as all instances of invalid or erroneous reasoning, being 
either an open or a concealed violation of the Laws of 
Thought, are necessarily extra dictionem, or independent of 
language. Then the most general division of them will be 
into Fonnal and Material Fallacies, "according as the 
source of deception lies in the act of Thought itself, or in 
the object upon which, or the circumstances under which, 
it is exercised." This distinction may be well expressed 
by saying that, in every Fallacy, the Conclusion either 
does, or does not, follow from the Premises. If it does not so 
follow, it is clear that the fault is in the reasoning, and in 
that alone ; the error concerns only the For7n of Thought, 
so that these alone are Logical Fallacies strictly so called. 
If the Conclusion does follow fi'om the Premises, we must 
search for the deception in the Matter of the Thought ; 
that is, we must consider what we are reasoning about, 
and what is the Conclusion which we wish to establish. 
Such consideration is properly extralogical ; but as the pur- 
pose of examining both classes of these Fallacies is the 
same, namely, to guard the mind against eiTor in its own 
processes, and as the consideration of only one class of Fal- 
lacies would very imperfectly answer this end, we subordi- 
nate strict method to convenience, and take into view all 
cases of defective and sophistical argumentation. While 
considering both of these classes of Fallacies, the ambi- 
guities of language which hide them, and which orig-inally 
led the reasoner astray, will incidentally come into notice, 
and the exposure of them thus effected will be, in a prac- 



272 OF FALLACIES. 

tical point of view, the most valuable result of the discus- 
sion. 

The subdivision of Fallacies in the Form of Thought, 
the Conclusion being illogically drawn, is easily effected, 
as it must have reference to the six General Rules, which 
are all embodied in Hamilton's one Supreme Canon of 
Mediate Inference. But the classification thus made is not 
easily adhered to, as it will often be found that the same 
Fallacy involves a violation of two or more of these Gen- 
eral Rules. The subject being once properly distributed 
into parts, however, the question is of little moment 
whether a particular case is rightly assigned to this or that 
class, if it may fairly be placed under either. The Rules 
most frequently violated are those which require, — 1. That 
a Syllogism should consist of only three Terms ; 2. That 
the Middle Term should be distributed in at least one of 
the Premises ; 3. That neither Term can be distributed in 
the Conclusion, if it was not taken universally in the Prem- 
ises ; 4. That the Conclusion must be Negative, if either 
Premise is Negative ; 5. That at least one Premise must 
be Affinnative. Besides the five Idnds of Fallacies arising 
fiom violations of these Rules, two others should be men- 
tioned, being the two invalid Moods of Hypothetical In- 
ference : — 6. From denying the Antecedent, or, 7. From 
affirming the Consequent, no Conclusion can be drawn. A 
number of other classes might be framed, arising from vio- 
lation of the various Rules of Immediate Inference, — the 
LaAvs of Conversion, Opposition, Infinitation, for instance. 
But as such errors are neither fi-equent nor insidious, they 
need not be considered here. 

1. To the class of Syllogisms which are invalid because 
they consist of more than three Terms may be referred all 
the cases which are usually placed under the head of ambig- 
uous Middle. If an ambiguous word or phrase is employed 
as the Middle Term in the Major Premise in one of its 



OF FALLACIES. 27S 

significations, and in the Minor Premise in a different sig- 
nification, it is evident that it does not afford us any means 
of ascertainincr the relation of the Extremes to each other. 
Having only compared A with M, and B with N, we can- 
not tell whether A is, or is not, B. Cases of this Fallacy 
are more numerous, and more apt to deceive, than those 
of any other class. They are the more insidious, because 
terms in frequent use, and which are constantly employed 
by the vulgar in ordinary conversation, are precisely those 
which are most apt to become ambiguous ; but on account 
of their familiarity, we fancy that we are perfectly ac- 
quainted with them, and therefore never suspect that they 
are leading us astray. 

Most political Fallacies are of this order. That very 
common phrase, the government^ means both " the system 
of laws under which we live and the machinery by which 
these are administered," and " the members of the ad- 
ministration for the time being, whose duty it is to carry 
out this system and to work this machinery " ; or it may 
mean certain measures, or a favorite policy, of these admin- 
istrators. Hence what Jeremy Bentham calls " the official 
malefactor's screen"; — "Attack us, you attack the gov- 
ernment." It may well happen that we best manifest our 
attachment to the government in the former sense, by a 
vehement opposition to it in the second meaning ; or, if the 
administrators are really able and well disposed, but are 
pursuing a mistaken policy in one respect, that we best 
show our regard for them personally, by laboring to con- 
vince them of their error. 

Still more ambiguous is that which is so much talked and 
written about, — the Church. How many controversies 
might have been spared, and how many volumes remained 
unwritten, had it been remembered that, at least in all 
countries where a religious establishment exists supported 
by law, " the Church " may have these six different 

12* R 



274 OF FALLACIES. 

meanings : — 1. a place of meeting for worship ; 2. all the 
people engaged as worshippers ; 3. only the faithful who, in 
in every age, since the advent of the Redeemer, have 
constituted the mystical Body of Christ; 4. the inferior 
clergy by whom the ceremonies of worship are conducted ; 
6. the superior clergy, who may be regarded as the heads 
of the Church ; 6. rules and customs respecting the modes 
of worship. As Bentham remarks, church is often made to 
mean churchmen, and law to signify lawyers, by the easy 
device of "substituting for men's proper official denom- 
ination the name of some fictitious entity, to whom, by 
customary language, and hence opinion, the attribute of 
excellence has been attached." 

If it were allowable to make a new use of one of Bacon's 
technical appellations, another large class of these sophisms 
might be called Fallacies of the Forum. These relate 
chiefly to money, currency, prices, mterest, py'ojits, and 
other tei'ms of frequent use in commercial and financial 
transactions. Money may mean either specie, or hank-notes^ 
or currency consisting of a mixture of these two, or credit, 
or capital, or that portion of capital which is offered for loan. 
An individual merchant is said to be in want of money 
wherewith to pay liis debts, when his only real lack is of 
credit, capital, or merchandise, money serving no other 
purpose in the affair than that of the carts by which the 
merchandise is transported. Again, interest is usually 
spoken of as if it were the Interest of money ; whereas a 
little reflection will satisfy any one, that money (if the 
name be apphed, as it usually is, to specie, to bank-notes, 
or to a combination of the two) yields neither profit nor 
interest ; whether it is in the hands of an individual or a 
corporation, whether in the pocket or in a safe, it Is a part 
of the owner's dead capital, and therefore he usually aims 
to get along with the use of as little of it as possible. 
Again, money Is usually considered as the measure of 



OF FALLACIES. 275 

wealth ; and then, by a very common metonomy, the meas- 
ure is confounded with the thing measured. Hence the 
following sophism, which may be said to have directed the 
commercial legislation of all civilized countries, down, at 
least, to the time of Adam Smith. 

Any increase of the money in a country is an equivalent enlarge- 
ment of its wealth. 

Laws to protect native manufactures against foreign competition 
tend to increase the money in the country. 

Therefore, such laws tend to increase the nation's wealth. 

But Adam Smith demonstrated that laws directed solely to 
keeping specie at home, only tend to make the country 
poorer ; and his arguments being at last generally admitted 
to be conclusive, there arose the opposite Fallacy of uni- 
versal Free Trade, which now controls the legislation of 
England, and is gaining ground in many other quarters. 

Laws which do not increase the quantity of money in the coun- 
try are at best useless. 
A Protective System does not increase this quantity. 
Therefore, a Protective System is useless. 

Of course, the answer to this argument is, that measures 
which do not prevent specie from going abroad may yet 
make the people more wealthy and prosperous, by ena- 
bling them, in their foreign trade, to exchange manufactures 
for raw material, — that is, the products of skilled labor 
for those of rude labor, — that is, again, the fruits of the 
industry of one man for those of the industry of three or 
four men. And it is precisely this system, — fostering the 
growth of native manufactures and allowing the produc- 
tion of raw material to take care of itself, — and not the 
prevalence of the doctrine of Free Trade, which has been 
the great source of England's prosperity. 

Another frequent source of this Fallacy — the introduc- 
tion, through the ambiguity of language, of four Terms into 



276 OF FALLACIES. 

a Syllogism — is the doctrine that the primaiy or etymo- 
logical meaning of a word is its only proper signification, or 
that it is the standard to which modern usage ought to con- 
form. This sophism is the more frequent, as it affords an 
opportunity for a httle display of erudition ; numerous 
instances of it can be found in what is otherwise an ingeni- 
ous and excellent work, Tooke's " Diversions of Purley." 
Thus, right comes from rectus^ and that from rego, — to 
rule or govern ; hence an alleged confirmation of the doc- 
trine of Hobbes, that right is only a creature of positive 
law, another unfounded assumption being then allowed to 
slip in, that the only kind of law is human, not divine. 
Again, most of the words which are now significant of the 
operations of Mind were originally applied to some of the 
forms or changes of Matter ; and this fact has been held to 
covmtenance the doctrine of materialism. But that spirit 
once signified breath, and animus, av6jjb0(i, air, does not 
afford even a presumption that such is their present mean- 
ing. The secondary or usual sense of a word has often 
travelled so far away from its primitive application as to 
have lost sight of it altogether, though we may be able to 
point out the stopping-places in its long joui'ney. 

I cannot help thinking that Sir William Hamilton has 
unconsciously glided into a Fallacy of this sort in his criti- 
cism of Dr. Reid's definition of memory. Reid says, 
" Memory is an immediate knowledge of things past " ; 
meaning thereby, as it seems to me, a present knowledge 
of the past. This, at any rate, is a very common use of 
the word ; an action is said to be immediate which takes 
place now, at once, or without delay. But immediate is 
also the opposite of mediate or vicarious; we are said to 
have an immediate knowledge of a thing when we know it 
directly or in itself, in contradistinction from knowing it 
vicariously, or through the medium of an image or repre- 
sentation of itself. In this sense, Hamilton argues veiy 



OF FALLACIES. 277 

properly that an immediate knowledge of the past is Impos- 
sible ; and Reid, I think, would have agreed with him ; 
while Hamilton would not have denied that memory is 
•present knowledge, or knowledge which exists at the present 
time. 

Another source of ambiguity, which is well exposed by 
Whately, is the supposition that paronymous or conjugate 
words — as the substantive, verb, adjective, and adverb 
formed from the same root — necessarily agree in mean- 
ing ; whereas, they often depart widely from each other in 
signification. Thus, what is imaginary is utireal ; but an 
image, as formed fi'om wood or stone, is a reality. To ap- 
prehend is to lay hold of, or to come to a knowledge of ; 
while apprehension often signifies /ear, dread. 

What Aristotle calls the Fallacy of Accent (he should 
have explained it as an ambiguity which may be resolved 
by accent) may be illustrated by the difference between 
gallant and gallant ; the fonner means Irave, high-spirited ; 
the latter, courteous or devoted to women. It is more diffi- 
cult to resolve by accent the curious ambig-uity of the 
phrase, not the least, where the two meanings are opposites 
of each other. Thus, " not the least difference " may 
mean either " no difference at all," or, " a very consider- 
able, perhaps the greatest, difference." In the former 
case, the phrase is elliptical, standing for " not any, not 
even the least, difference." The least is excluded or nega- 
tived, as in the phrase "woi the least," both by nothing 
and by the greatest. 

As De Morgan remarks, "a statement of what was said, 
with the suppression of such tone as was meant to accom- 
pany it, is the fallacia accentus. Gesture and manner often 
make the difference between irony or sarcasm and ordi- 
nary assertion. A person who quotes another, omitting 
anything which serves to show the animus of the meaning; 
or one who without notice puts any word of the author he 



278 OF FALLACIES. 

cites in Italics, so as to alter its emphasis ; or one wlio 
attempts to heighten his own assertions, so as to make 
them imply more than he would openly say, by Italics, or 
notes of exclamation, or otherwise, is guilty of the fallacia 
accentus.^^ 

2. The Fallacy of Undistributed Middle does not occur 
so frequently, and is not so insidious, as that of Ambiguous 
Middle. We may fall into it unawares by overlooking 
the difference between the Collective meaning of the word 
aZZ="all taken together," and its Distributive meaning, 
in which all signifies " each and every." Thus, all the 
Senators (taken collectively) try impeachments ; all the 
Senators (i. e. each and every Senator) are chosen by the 
State legislatures. 

All these exercises will fatigue me ; 
This performance is one of them ; 
Therefore, this performance will fatigue me. 

Another ambiguity, which may serve to cloak this logical 
fault, is passing from the Composite to the Divisive, or from 
the Divisive to the Composite, meaning of a proposition. 
If we take together those members of the sentence which 
ought to have been taken separately, it is called the soph- 
ism of Composition ; if we take separately what is true of 
all only when they are united, it is the sophism of Division. 
A ludicrous instance of the latter is found in most of the 
old text-books on Logic. 

Two and three (taken compositely) are five ; 

Two and three (taken divisively) are odd and even ; 

Therefore, five is odd and even. 

An instance of the former is what may be called the 
Spendthrift's Fallacy. 

All of these contemplated expenditures (taken separately) are 
of trifling amount ; 

Therefore all of them may be incurred (together) without ruin- 
ing me. 



OF FALLACIES. 279 

The lazy person reasons in the same manner, in respect 
to the waste of an hour or two of time, or to missing this 
or that favorable opportunity. It behooves such persons 
to remember, that the predesignation any one is not the 
equivalent of all taken collectively. 

This is the nature of the famous old Fallacy called 
<TQ)p6'i, a heap, whence the name Sorites applied to a differ- 
ent and legitimate argument. Does one grain of corn 
make a heap? No. Do two grains make a heap? No. 
Do three grains ? No. And in like manner, we may ask 
a series of questions, successively adding unity to the num- 
ber, till the respondent is at last obliged to contradict him- 
self, and confess what he has just denied, that a single 
grain of corn makes the only difference between what is 
not, and what is, a heap. The same sophism was denom- 
inated by the old logicians the Calvus, because illustrated 
by a series of questions beginning with the inquiry, whether 
pulling one hair out of a man's head made him bald. 
Horace used it to I'idicule the fashion of valuinsc ancient 
authors simply on account of the antiquity of their pro- 
ductions. 

" Iste quidera veteres inter ponetur honeste, 
Qui vel mente brevi vel toto est junior anno, 
Utor permisso, caudseque pilos ut equinse 
Paulatim vello, et demo unum, demo etiam unom, 
Dum cadat elusus ratione mentis acervi, 
Qui redit ad fastos, et virtutem aestimat annis, 
Miraturque nihil nisi quod Libitina sacravit." 

But while laughing at an old sophism, we may be found 
ridiculing a modern paralogism. I have recently heard 
this very argument gravely reproduced in a learned Acad- 
emy, during a debate on an important question of science. 
The answer to it is obvious ; — not one alone, but one added 
to the previous 999, constitutes a heap. 

The Fallacy of the Composite and Divisive sense is apt 
to be repeated by the mcautious in estimating the proba- 



280 OF FALLACIES. 

bility of two events happening conjointly. Though each 
of them, taken separately, is more likely than not to 
happen, the probability of their occurrence together is 
of a very inferior character. Thus, the probability of the 
first being represented by |^, and that of the second by -|, 
that of their joint occurrence is the froduct of these two 
fractions, or ^S, or much less than ^, which represents 
an even chance. So we are often misled by the use of 
the word tendency. We rightly say that a given result 
tends to happen only when there is more than an even 
chance of its occurrence ; if there is less than an even 
chance, it tends not to happen. This is the form of a com- 
mon blunder in the docti-ine of means or averages. Thus, 
all persons who have attained the age of twenty-four sur- 
vive on an average till they are sixty-two years old. But 
no one person^ now aged twenty-four, has a right to expect 
that this average will be exemplified in his particular case. 
On the contrary, his chance of attaining the precise age of 
sixty-two, no more and no less, is very much less than his 
chance of dying at some other age. All (collectively) tend 
to the average ; but no one tends to the average. This is 
no paradox; for the average is only a compensation of 
errors, and therefore remains the same whether the errors 
are great or small, provided only that they are equally dis- 
tributed on all sides of the average; and such equality of 
distribution is the direct consequence of the fact, that no 
one error has any tendency to be on one side of the average 
rather than on any other side. No one tends to the aver- 
age, but tends equally, or indifferently, to depart from it. 

Mr. Darwin, in his theory of " the Origin of Species by 
Natural Selection," is guilty of both of these forms of the 
Fallacy. He first argues, that the specific Marks of Spe- 
cies, both in the animal and vegetable kingdoms, tend to 
vary, because, perhaps in one case out of ten thousand, a 
child is born with six fingers on one hand, or a cat with 



OF FALLACIES. 281 

blue eyes, or a flower grows out of the middle of another 
flower. Collecting many instances of such sports of nature 
or monstrosities, he bases his whole theory upon them, for- 
getting that the vastly larger number of normal growths 
and developments proves that the tendency is to non-varia- 
tion. Then, secondly, because perhaps one out of a hun- 
dred of these abnormal Marks is transmitted by inheritance, 
he assumes that these freaks of nature tend to perpetuate 
themselves in a distinct race, and thus to become perma- 
nent Marks of distinct species. Thirdly, as either of the two 
preceding points, taken singly, affords no basis whatever 
for his doctrme, he assumes that their joint occurrence 
is probable, because he has made out what is, in trutli, a 
very faint probability that each may separately happen. 
But if the chance of a variation in the first instance is only 
one out of a thousand, and that of the anomaly being 
handed down by descent is one out of a hundred, the 
probability of a variation established by inheritance is but 
one out of a hundred thousand. As the theory further 
requires the cumulation of an indefinite number of such 
variations one upon another, the formation of a new species 
by the Darwinian process may be safely pronounced to be 
incredible. 

3. The third class of Fallacies, those which arise from a 
violation of the Rule that neither Term must be distributed 
in the Conclusion if it was not distributed in the Premise, 
are frequent enough, but will deceive no one if they are 
not ambiguously expressed. If it is the Predicate of the 
Conclusion which is illogically distributed, the error is 
called an Illicit Process of the Major Term ; if the Sub- 
ject, an Illicit Process of the Minor Term. Of these, the 
former is more common and insidious ; for as the Quantity 
of the Predicate is not expressed in the ordinary use of 
language, we are apt to forget that, in a Negative propo- 
sition, it is always presumed to be Universal, and in an 



282 OF FALLACIES. 

Affirmative, if nothing be said to the contrary, it is uBually 
Particular. In what the Aristotehans call Indefinite prop- 
ositions, the Quantity of neither Term is expi'essed ; but if 
Affirmative, both Terms are commonly understood to be 
distributed ; for most propositions of this sort are either 
Definitions, or statements of a general law ; and in both of 
these cases, the Universal quantification of each Term is 
easily supplied in thought. Thus, Falsehood is wilfid decep- 
tion^ is easily and properly construed to mean. All falsehoods 
are all wilful deceptions ; and Matter gravitates^ to mean, All 
matter is all that gravitates. But statements of a general 
law must be carefully distinguished fi'om statements of the 
application of such a law to a particular class of cases ; 
thus, Stones gravitate^ means only, '•'■All stones are some 
gravitating substances." 

All birds are winged ; 
The bat is not a bird ; 
Then the bat is not winged. 
Here, the Conclusion is logically false, for it contains an 
Illicit Process of the Major Term. The Sumption is un- 
derstood to mean only that " All birds are some winged 
things " ; the bat, therefore, though not a bird,, may be 
(as here it happens actually to be) one of the other some 
winged things, while the illogical Conclusion declares it to 
be not (any^ winged thing. 

No slave has his rights ; 

All slaves are persons of African descent ; 

Therefore no person of African descent has his rights. 
The Illicit Process is here of the Minor Tenn ; for the 
Conclusion denies of aw?/, what the Premises authorize us 
to deny only of some Africans. 

In both these cases, the Fallacy is so obvious that it can- 
not deceive any one who thinks cleai'ly. But the ambigui- 
ties of language may so cloak the deception as to render 
its exposure difficult. Most insidious in this respect is the 



OF FALLACIES. 283 

ambiguity between what is true ahsolutely^ and what is 
true only in some respect, to dirXw'i ?) fir] d'Tr\w<;. From 
this confusion of language two modes of false reasoning 
result, the first of which is denominated by the Aristo- 
telians the fallacia a dieto secundum quid ad dictum sim- 
pliciter. It consists in inferring something as true of tho 
subject simply, or without limitation, w^hich is true of it only 
in some respect. Thus, Man is immortal (in respect to his 
soul) ; therefore, man is immortal (absolutely, both as to 
soul and body). The second has been called the fallacia 
accidentis, because it confounds an accidental attribute with 
what \& essential or principally intended. But as it is the 
exact converse of the former, it should rather be called the 
fallacia a dicto simpliciter ad dictum secundum quid. Thus, 
to take the converse of the former instance, Man is mortal 
(man being here understood, as usual, to be a living or- 
ganism) ; therefore, man is mortal (as respects his soul). 
Aristotle gives the following illustration, which is puerile, 
though it might well puzzle a begmner : — 

Socrates is not Coriscus (in any sense) ; 

But Coriscus is a man (this being one of his characteristics) ; 

Therefore, Socrates is not a man. 

The most difficult cases to be resolved are those In 
which giving the name of the genus, to which the subject 
belongs, is confounded with giving the name of its species. 
Thus, 

He who calls you a man speaks truly ; 
He who calls you a knave calls you a man ; 
Then he who calls you a knave speaks truly. 
A ludicrous instance of the former mode of the Fallacy is 
found in most of the text-books : — 

What you bought yesterday you eat to-day ; 
But you bought raw meat yesterday ; 
Then you eat raw meat to-day. 
Perhaps both forms of this Fallacy are best resolved by 



284 OF FALLACIES. 

considering that the ambiguity resides In the Copula. 
When one thing Is predicated of another, It Is seldom un- 
derstood that the Predicate Is thereby entirely identified 
with the Subject, as the proposition would then be merely 
tautologous, A is A. But unless It is so identified, we can- 
not affirm of the Predicate all that might be affirmed of the 
Subject. The logical rule as usually enounced, that no 
Term must be distributed In the Conclusion If It was not 
distributed in the Premises, Is defective ; for it only insures 
that the Quantity shall be the same. The sense ought also 
to be the same throughout, whether absolute or relative, 
whether In one respect or In many, whether essentially or 
accidentally. An adequate enouncement of the rule would 
be, that no more mid no less^ in any respect^ must be collected 
in the Conclusion than was given out In the Premises. In 
order to know how much was so given out, we must consider 
the meaning of the Copula, is^ in each separate case. Mr. 
De Morgan says : " The most common uses of the verb 
are, — 1. absolute identity, as in 'the thing he sold you 
is the one I sold him,' — this Is the dictum simplidter ; 
2. agreement In a certain particular or particulars under- 
stood," dictum secundum quid, " as in ' he is a negi'o,' said 
of a European in reference to his color ; 3. possession of a 
quality, as in ' the rose Is red ' ; 4. reference of a species to 
Its genus, as in ' man is an animal.' All these uses are 
independent of the use of the verb alone, denoting exist- 
ence, as In 'man is [I. e. exists].'" In most cases, these 
meanings are not interchangeable ; and whenever they are 
not, a Fallacy may be founded upon the difference between 
any two of them. 

But the enumeration is imperfect ; several additions may 
be made to It, by observing, what has been already re- 
marked in ti'eating of Contradiction, " that two Judgments 
properly contradict each other only when that which is 
affirmed by the one is denied by the other, — 1. in the 



OF FALLACIES. 285 

same respect ; 2. in the same manner ; 3. in the same 
degree ; 4. at the same time." Thus, Mr. De Morgan's 
instance of absohite identity is unhappily chosen ; for if the 
hmitation of time is taken into account, " the horse which 
he sold you," being ten years old, is not absolutely the same 
horse which I sold him, as that was only six years old. 
All Fallacies of this class may be easily resolved by merely 
completing in expression what was previously only implied 
in thought. We thereby prevent any more or less stress 
being laid upon an accident, or upon any view of the sub- 
ject, in the Conclusion, than was done in the Premises. 

The use of wine is destructive to the health ; 

Therefore its use ought to be forbidden. 
As stated, this Enthymeme may seem indisputable ; but 
there can be no practical application of it, unless it is under- 
stood to mean that any use of wine is pernicious, and hence 
that it ought ahvays to be forbidden. This is the fallacy 
of arguing against the use of a thing merely from its liabil- 
ity to abuse. The proper caution is, that no change what- 
ever in the Terms employed must take place during the 
process of inference. 

In ordinary language, few terms are so loosely used, or 
so often improperly applied, as the same, all, always, &c. 
Hence the logicians were obliged to form a separate class 
of Fallacies, which they called those fictce universalitatis. 
People say the same, when they mean similar ; all, when 
they mean only most; and always signifies to them the 
same ^?, frequently. They do not even mention the excuse 
which the Psalmist alleges when conscious of his exaggera- 
tion, — "I said in my haste. All men are liars." It was 
once considered a difficult question, whether a stocking, 
which had been so much darned that not a thread of the 
original fobric remained, was, or was not, the same stocking. 
But it can present no difficulty to one who considers that 
sameness or identity is an absolute term, which can neither 



286 OF FALLACIES. 

be affirmed nor denied except in an unqualified sense ; and 
that all which can be truly predicated of what comes short 
of sameness is similarity. 

" We might suppose that most persons have no idea of a 
universal proposition ; but use the language, never intend- 
ing all to mean more than most. And in the same manner, 
principles are stated broadly and generally, which the 
assertor is afterwards at liberty to deny, under the phrase 
that he does not carry them so far as the instance named. 
It would not do to avow that the principle is not always 
true ; so it is stated to be always true, but not capable of 
being carried more than a certain length. Are not many 
persons under some confusion about the meaning of the 
word general f In science, it always has the meaning of 
universal; and the same in old English. Thus the Cate- 
chism of the Church of England asserts that there are two 
sacraments which are generally [universally] necessary to 
salvation, — meaning, necessary for all of the genus in ques- 
tion, be it man. Christian, member of the Church, or any 
other. But in modern and vernacular English, general 
means only usual, and generally means usually.''"' * 

An opposite error, but one proceeding from the same 
source, viz. from confounding the Universal with the Par- 
ticular, is committed by many Americans and some Eng- 
lishmen in respect to the word quite. Its proper meanmg 
is completely, entirely, as " quite contrary principles " ; but 
it is often used in the sense of very, as " quite warm," 
" quite cold," " quite recent." 

The word same, in ordinary parlance, is applied to all 
objects for which a single description will serve, or which 
are included under one Concept. Thus we say, " This 
writing is on the same paper with that," meaning the 
same hind of paper ; " This erroneous reasoning is the same 
Fallacy with the other," meaning the same kind of Fallacy. 

* De Morgan's Formal Logic, p. 272. 



OF FALLACIES. 287 

A description or Concept, as we have seen, is an imperfect 
enumeration of the quahties of a whole class of objects ; 
and it is only because the enumeration is imperfect that 
many can be ranked under one class. A perfect enumera- 
tion, if such were possible, — a list of all the qualities, — 
would cause each Individual (if this were not a contradic- 
tion in terms) to constitute a class by itself. 

" Nothing, perhaps," says Dr. Whately, "has contributed 
more to the error of Realism, than inattention to this ambi- 
guity. When several persons are said to have one and the 
same opinion, thought, or idea, many men, overlooking the 
true, simple statement of the case, which is, that they are 
all thinking alike [or similarly'\, look for something more 
abstruse and mystical, and imagine there must be some one 
thing, in the primary sense, though not an Individual, 
which is present at once in the mind of each of these per- 
sons; and thence readily sprung Plato's theory of Ideas, 
each of which was, according to him, one real, eternal 
object, existing entire and complete in each of the Indi- 
vidual objects tliat are known by one name.* Hence, first 
in poetical mythology, and ultimately, perhaps, in popular 
behef. Fortune, Liberty, Prudence (Minerva), a Boundary 
(Terminus), and even the Mildew of Corn (Rubigo), be- 
came personified, deified, and represented by statues ; 
somewhat according to the process which is described by 
Swift, in his humorous manner, in speaking of Zeal, in the 
' Tale of a Tub,' ' how fi'om a notion it became a word, 
and thence, in a hot summer, ripened into a tangible sub- 
stance.' " 

But Dr. Whately seems to depart from his own prin- 

* " When abstract truth is contemplated," asks Dr. Price, " is not the 
very object itself present to the mind ? When millions of intellects contem- 
plate the equality of every angle in a semicircle to a right angle, have they 
not all the same object in view ? Is this object nothing? Or is it only an 
image or kind of shadow ? These int^uiries carry our thoughts high." 



288 OF FALLACIES. 

ciples, when lie proceeds to remark, that " Sameness, In 
the primary sense, does not even necessarily imply Simi- 
larity ; for if we say of any man that he is greatly altered 
since such a time, we understand, and indeed imply by 
the very expression, that he is one person, though different 
in several qualities; else it would not be Ae." Siu*ely, 
what we mean by Personal Identity is sameness of sub- 
stance under great differences of phenomenal manifestation. 
Sameness here does not imply Similarity, merely because 
it impHes a great deal more ; — namely, absolute oneness 
of substance, under the greatest diversity of outward ap- 
pearance. The Person is not different at difterent times, 
but his attributes and actions are. But perhaps this is 
what Dr. Whately really means, though it is not the ob- 
vious construction of his language. He seems to consider 
the Person, and his outward character or manifestation, as 
one. 

The Fallacy of over-hasty generalization is very frequent, 
as Bentham remarks, in political reasoning. It consists in 
attributing to an individual person or thing certain attri- 
butes which appear in many or most others which have 
been loosely ranked in the same class with the object in 
question, and thereby designated by the same name. Thus, 
a pamphlet entitled " The Crimes of Kings" was published 
in Paris in 1792, in order to prove that Louis XVI. ought 
to be put to death. In like manner, " The Cruelties of 
Catholics " was the title of a book published in England as 
an argument against CathoHc Emancipation. Most polit- 
ical harangues abound in arguments of the like character ; 
but they are evidently addressed to the passions rather 
than the intellect, as they cannot deceive any one who is 
cool enough to be able to think. 

To the ambiguity between what is true absolutely, and 
what is true only in some respect, may be referred the 
famous sophism of Eubulides, called Wevhofievo^, the Liar. 



OF FALLACIES. 289 

According to Diogenes Laertius, Chiysippus the Stoic wrote 
six different treatises upon this logical puzzle, and Philetas 
of Cos studied himself to death in the vain attempt to solve 
it. " If you say that you He, and say so truly, then you 
do lie ; but if you say so falsely, then you speak the truth. 
In either case, therefore, the same assertion is both true 
and false." But if any one says, " I lie," his assertion is 
not a dictum simpliciter ; for a lie is only possible secundum 
quid. He who lies must lie about something, in some par- 
ticular affirmation or denial ; otherwise, his assertion is as 
meaningless as the remark that " something is very like." 
Like what ? * If he means only, " I have lied in some 
former assertion," there is no contradiction ; if he means, 
" I lie now, in saying that ' I lie,' " he really makes two 
affirmations, of which the one, the oratio obliqua, is vague 
and meaningless, and the other, the oratio directa, improp- 
erly characterizes this one as a falsehood, — improperly, for 
that which has no significance cannot be either true or 
false. 

This sophism has been stated in a different and inferior 
form, as follows : — 

*' All the Cretans are liars." 

But Epimenides, who says this, is himself a Cretan. 

Therefore, as he is a liar, this saying is not true. 

But if the saying is not true, Epimenides may have spoken the 

truth. 
Then the saying is true ; — and so on, as before. 

But here the Major Premise does not support the Con- 
clusion, unless it is construed to mean that the Cretans are 
always liars, — that they cannot speak the truth. And 
even if this were true, one who is himself a Cretan could 
not say so, for then he would speak truly, and so contra- 
dict himself. Of a similar nature is the following puzzle. 

* Hansel's Notes to Aldrich, p. 145. 
13 8 



290 OF FALLACIES. 

" No rule holds true Avitliout some exceptions." 

But this very remark is a rule. 

Then it has exceptions. 

Then there are rules without exceptions. 

Here the reasoning, as such, is correct, and the absurd- 
ity to which it leads demonstrates what has been properly 
called the Fallacy of universal scepticism. As Sir James 
Mackintosh remarks, " universal scepticism involves a con- 
tradiction in terms ; it is a belief that there can be no 
belief." He who denies ever^/ assertion thereby denies his 
own denial, and so contradicts himself. The Major Pre- 
mise in this very puzzle is such a self-contradictory asser- 
tion ; I cannot make a true general remark, that all general 
remarks are false ; or, what is the same thing, that they 
" have exceptions." 

4 & 5. Little need be said to illustrate the remaining 
classes of Fallacies, as they are of infrequent occurrence, 
and are easy to be detected unless cloaked by some of the 
ambiguities of language which have already been exposed. 
Those which respect the Quality of the reasoning may well 
be considered together. The two Rules are, that at least 
one of the Premises must be Affirmative, and that the Con- 
clusion must be Negative if either Premise is Negative. 
These Rules may be violated in appearance, when they are 
not so in reality. For instance : — 

No one is rich who has not enough ; 

No miser has enough ; 

Therefore no miser is rich. 

Here, both Premises are seemingly negative ; but they 
are not really so, for the negation of having enough is a 
part of the Predicate, and therefore does not affect the 
Quality of the Judgment, which depends on the Copula. 
Instead of not having enough, substitute the equivalent 
phrase, wanting more, and the seeming incorrectness is 
removed. 



OF FALLACIES. 291 

No one who wants more is rich ; 
Every miser wants more ; 
Therefore no miser is rich. 

As has been shown in treating of Exponibles, the Ex- 
clusive proposition, " None but Whites are civilized," is 
really complex ; it contains one direct assertion, respecting 
all non- Whites, that they are not civilized, and one implied 
assertion, that some Whites are civilized. Then the follow- 
ing syllogism is valid, though each of its three Judgments 
appears to be negative. 

None but Whites are civilized ; = No non- White is civilized ; 
The Hindoos are not Whites ; = The Hindoos are non-WIiites ; 
The Hindoos are not civiUzed. 

Two ludicrous instances, which have often been repeated 
in the books, are enough to illustrate the Fallacy which 
arises from a violation of the fifth Rule, though both of 
them can be referred also to one of the other classes which 
have been already considered. 

Nothing is heavier than platinum ; 
Featliers are heavier than nothing ; 
Therefore, feathers are heavier than platinum. 

This sophism cannot puzzle even a beginner, and is of 
the same character in the following. 

No cat has two tails ; 

Every eat has one tail more than no cat ; 

Therefore, every cat has three tads. 

The Fallacy plurium interrogationum, as it was called, 
may be brought under this head by being referred to the 
ambiguous construction of sentences. It is a mere trick, 
which consists in asking two or more questions as if they 
■were one ; then the respondent is entrapped whether he 
answers in the Affirmative or the Negative, as either will 
be inappropriate to one or the other of the two interroga- 
tories. Of course, the Fallacy is solved by dividing the 



292 OF FALLACIES. 

questions and answering them separately. The standard 
illustration is asking a man " whether he has ceased beating 
his father." Lawyers are often guilty of this sophism 
while examining a witness in court, by insisting that he 
shall give what they call " a categorical answer " ; — that 
is, that he shall say either Yes or No. But to the question 
as they propound it, either Yes or No will be a false 
answer. A question often involves a real duplicity under 
a seeming unit}^, as the uncertainty may regard, not the 
meaning^ but the extension, of the Terms employed ; and the 
same ambiguity may lurk in a categorical proposition, or in 
the answer to an interrogatory. The distinction between 
Contraries and Contradictories, and the relation between 
Sub-Contraries, must be kept in view. He who denies 
that all are lost, does not thereby deny that some, perhaps 
many, even all hut one, have perished. Some are not may 
mean perhaps all are not, or some certainly are. To assert 
or deny a particular motive for an action, is still to leave the 
question undecided as to the concurrence of many motives, 
and to say nothing about their comparative strength. 
Most of our actions proceed from a mixture of motives, 
and the agent himself may not be able to say which was 
the principal. Men easily deceive themselves in this 
respect, as their memory, their vanity, or even their re- 
morse, may mislead them ; and the mistake is especially 
frequent when conscientious or religious motives are in 
question. 

Those who made it their business to invent logical puz- 
zles, and to entrap an opponent in dispvitation, often secured 
their Premises beforehand, by requiring their interlocutor 
to answer a series of questions. Socrates was a great mas- 
ter of this eristic art ; but though it may fairly and profita- 
bly be employed in the communications of a teacher with 
his pupils, a free use of it may reduce an opponent to silence 
without convincing him. In Plato's Dialogues, Socrates 



OF FALLACIES, 293 

often appears in no better light than a satirical disputant 
quibbling about the meaning of words. The following 
instance of the Fallacy plurium interrogationum, which 1 
borrow from Fries, would not puzzle any one if it were not 
stated in the form of questions and answers. 
Is it not true tliat you must have lost that which you once had, 

but which you have no longer ? Yes. 
Did you not have ten counters when you commenced the game ? 

Yes. 
Have you ten counters now ? No. 
Then you have lost ten counters. 

But he still had eight, having lost only two ; to deny 
possession of the whole is not necessarily to deny that you 
have a part. But if obliged to answer simply Yes or No, 
the respondent could not avail himself of this distinction. 

6 «& 7. From Dr. Whately's convenient collection of 
" examples for the exercise of learners," to which I have 
been indebted for several of the preceding illustrations, I 
borrow the following instances of violation of the Canons 
of hypothetical reasoning. 

If penal laws against Papists were enforced, they would be ag- 
grieved ; 
But they are not enforced ; 
Therefore, the Papists are not aggrieved. 

Though this argument was often gravely repeated m 
Parliament, and elsewhere, during the debates on Catholic 
Emancipation, it is, of course, entirely invalid by the rules 
of Logic ; for from denying the Antecedent in a Hypo- 
thetical Judgment, no Conclusion follows, since the Conse- 
quent may still be true from some other reason than the 
one here specified. In this case, though the penal laws 
were not enforced, the Catholics had a right to feel ag- 
grieved that these laws should be permitted to remain in 
the statute-book, as this was an insult to them personally, 
and to their faith. 



294 OF FALLACIES. 

"We ought to give one day in seven to religious duties, if the 

Fourth Commandment is obligatory on us ; 
But we are bound to set apart one day in seven for religion ; 
Therefore, the Fourth Commandment is obligatory on us. 

The Canon here violated is, that from affirming the 
Consequent no Conclusion can be dravi^n, since the Conse- 
quent may have resulted from some other reason than that 
specified in the Antecedent. A little attempt is here made 
to cloak the Fallacy, by inverting the natural position of 
the Antecedent and the Consequent in the Major Premise. 

We pass now to a consideration of those fallacious rea- 
sonings which are correct in Form, since the Conclusion is 
logically drawn, but are faulty in Matter, either from some 
error or undue assumption in the Premises, or some mis- 
take as to the point to which the argumentation ought to 
be directed. An exhaustive classification of Material Fal- 
lacies is not to be expected, as they are numerous and 
varied in form, and derive then' characteristics chiefly from 
the particular Matter of the special sciences which first 
suggested them. The only proper classes of them which 
have been separately considered by logicians are those 
which, ever since Aristotle's time, have been technically 
designated as the petitio princvpii^ the ignoratio elenchi, and 
the non-causa pro causa ; to which may be added several 
miscellaneous sophisms of so puzzling a character that the 
old logicians called them the Inexplicables. 

1. The vulgar equivalent for petitio principii is begging 
the question; and the common explanation of it is, that it 
consists in assuming, in the course of the argument, the 
very point which ought to be proved. Its most deceptive 
application is what is called reasoning in a circle, in which 
Premises are first assumed, and subsequently proved by 
means of the very Conclusions which they had been used 
to establish. This error is more difficult of detection in 
proportion as the circle is more extended, or as more Syl- 



OF FALLACIES. 295 

Iogisni8 are employed before the reasoner Comes round to 
the veiy point that he started fi'om. As Krug remarks, 
*' to the Circle there are properly required two probations, 
which are so reciprocally related that the Antecedent in 
the one is proved by its owti Consequent in the other. 
The proposition A is true because the proposition B is 
true; and the proposition B is true because the proposition 
A is true. A Circle so palpable as this would, indeed, be 
committed by no one. The vice is usually concealed by 
the interpolation of intermediate propositions, or by a 
change in the expression." "Thus," says Hamilton, "Pla- 
to, in his Phcedo, demonstrates the immortality of the soul 
from its simplicity ; and, in the Republic, he demonstrates 
its simplicity from its immortality." Theologians, also, 
sometimes fall into this error, by first proving the authority 
of the Church from the testimony of the Scriptures, and 
then seeking to establish the authenticity of the Scriptm'cs 
by the testimony of the Church ; and the Fallacy escapes 
notice, because one branch of it is found, perhaps, in a 
polemic tract on Church government, and the other half in 
a treatise on the Evidences. 

Strictly speaking, all valid reasoning proceeds ex con- 
cessis. Two Premises must be assumed, or taken for 
granted ; and these two, taken in conjunction, necessarily 
involve the Conclusion. Thus much must be conceded to 
those who claim that every Syllogism presupposes the truth 
of what it is brought forward to establish. But then it is 
presumed that there is no undue assumption; — that the 
two Premises, which we now posit, either have been al- 
ready proved, or that they are imiversally admitted truths, 
or that they have just been conceded, pro hac vice, by the 
opponent. As Mr. Mansel remarks, " the petitio princijni is 
a material, not a formal Fallacy, and consists in assuming, 
in demonstration, a non-axiomatic principle as axiomatic, 
or in dialectic disputation, a non-probable principle as prob- 



296 OF FALLACIES. 

able." It consists not in mere assumption, then, for that 
is necessary, but in U7idue assumption. That branch of it 
which is called reasoning in a circle is, from the nature of 
the case, not a vice which can be committed in a sino;le 
Syllogism, but only in a series of Syllogisms constituting a 
chain of proof. That which vitiates a single Syllogism is 
reasoning from Premises, one, if not both, of which either 
is in more need of proof than the very proposition wliich 
we seek to prove by it, or it is that proposition itself 
only veiled in other words, or it assumes two Terms to 
be mere equivalents of each other, when they really have 
not the same meaning. We must not reason like the 
physician in MoliSre, who accounts for opium producing 
sleep by saying that it has a soporific virtue. The ai'gu- 
ment that locomotion is not an attribute of all animals, since 
sponges cannot change their place, contains the undue as- 
sumption that sponges are animals. Indeed, the Fallacy 
in this case becomes obvious when the argument is expli- 
cated into a regular Syllogism. And this is usually so in 
what is popularly called begging the question ; the argument 
is stated as an Enthymeme, and the suppressed Premise is 
that which contains the undue assumption. 

A petitio principii is involved in every case of reasoning 
which depends upon an Imperfect Disjunction, though such 
cases might also be properly refen'ed to other kinds of 
Fallacy. A Disjunction must be assumed to be perfect, or 
the Dilemma which is founded upon it is obviously invalid. 
Of this character is the famous sophism of Diodorus Cro- 
nus, which professes to demonstrate the impossibility of 
motion, and which has probably occasioned more discus- 
sion than any other logical puzzle on record. It occupies 
a high place among those w-liich were formerly called the 
Inexplicables. Dr. Whately seems tacitly to admit that it 
is insoluble ; for, though he justly criticises an attempted 
explanation of it by Aldrich, he proposes nothing to take 
its place. The sophism may be thus stated. 



OF FALLACIES. 297 

If motion is possible, a body must move either in the place where 

it is, or in a place where it is not. 
But a body cannot move in the place where it is ; and of course, 

it cannot move where it is not. 
Therefore, motion is impossible. 

It is hazardous to differ from Mr. Mansel upon any logi- 
cal question ; but the solution of this sophism which he has 
adopted and improved seems to me unsatisfactoiy. He 
says, " The true solution is, that the disjiuictive premise is 
false. ' The place where a body is,' is contradictory of 
* the place where a body is not ' ; as ' Englishmen ' is con- 
tradictory of ' not-Englishmen ' ; but ' moving in the place 
where it is,' is no more contradictory of ' moving in the 
place where it is not,' than ' an army composed of English- 
men ' is contradictory of ' an army composed of not-Eng- 
lishmen.' As it would be false to say, ' Every army must 
be composed of Englishmen or not-Englishmen,' to the ex- 
clusion of the third possibility of a mixed force, so it is 
false to say, ' Every body must move in the place where 
it is, or in the place where it is not,' to the exclusion of 
the third possibility of moving partly in the one and partly 
in the other. This solution is substantially given by 
Hobbes." * 

Hobbes even gives a diagram to prove that a body — 
quantulumeunque sit^ however small it may be — " cannot, 
all at once, so leave the whole of its former place that a 
jyart of it shall not he in that portion which is common to 
the two places^ namely, the one which is left and the other 
which is reached." But the difficulty cannot be thus 
evaded. A part of a body cannot be in two places at once, 
any more than the whole. For suppose that which moves 
to be a mathematical point, as in the geometer's conception 
of the generation of a line. Such a point, of course, being 
indivisible, cannot be " partly in the one and partly in the 

* Mansel's Notes to Aldrich, p. 144. 
13* 



298 OF FALLACIES. 

other " place. A whole cannot move unless every point in 
it moves also. Every individual must be, as Mr. Mansel 
acknowledges, either an Englishman or a not-Englishman. 
Reduce the army to a single soldier, and the difficulty of 
moving him, according to this sophism, is still insuperable. 

The following solution, I believe, has not before ap- 
peared in print. The Major Premise of the sophism is not 
true except with a proviso or limitation, which is improperly 
suppressed ; so that the Fallacy may properly be referred 
to the class a dicto secundum quid ad dictum simplidter. 
" A moving body, at any one indivisible moment, must be 
either where it is, or where it is not." When the proviso 
here italicized is expressed, the proposition is true, the 
reasoning is sound, and the conclusion is correct. In any 
one indivisible moment, motion is impossible ; for motion re- 
quires time as well as space. The Axiom of Excluded 
Middle, that a thing must be, or not be, in a certain place, 
does apply to a body ; but it does not apply to a moving 
body, and this is what covers up the Fallacy. For in order 
to be moving, it must, at the second indivisible instant, be 
where it was not at the first instant. Hence, we do not 
violate the Axiom when we deny the Major Premise as 
originally stated ; for " a moving body " is that which Jias 
been where it now is not. The difference of tense (time) 
makes it possible for the same thing to be and not to be. 
The law of Excluded Middle itself, as we have seen, is true 
only when the qualification at the same time is understood. 

A solution which is substantially similar to the one here 
given is proposed by Mr. De Morgan. Movement is 
change, and so requires two places ; a body is not moved in 
a place, hnifrom one place to another. 

2. Ignoratio elenchi is what we should now call answer- 
ing to the wrong point. It is proving something Avhich 
does not really controvert your antagonist's position, though 
it is assumed to do so. An Elenchus is a Syllogism which 



,a i 



OF FALLACIES. 290 

will confute the argument of your opponent ; and ignoratio 
elenchi is ignorance of what will so confute him, — igno- 
rance of the fact that your Conclusion, even if it were 
established, would not contradict his Conclusion. This 
eiTor in reasoning is so common, that special precautions 
have, in some cases, been adopted in order to obviate it. 
Thus, in Law, the only object of what is called special 
pleading is, to ascertain the precise point at issue, or to 
prevent irrelevancy of evidence and argument by binding 
both parties in the suit to address themselves to what is 
really the sole point in controversy. A Demurrer has been 
happily explained to be equivalent to the remark, " Well, 
what of that?" Even granting the facts stated in the 
declaration to be tnie, it may be insisted that these facts 
give the plaintiff no ground of action ; and hence, that it 
was an ignoratio elenchi to state them at all. 

As the Port Royal logicians remark, the passions of men 
afford the reason why this sophism is so common in con- 
troversy. " We dispute with warmth, and often without 
understanding one another. Passion or bad faith leads us 
to attribute to our adversary that which is veiy far from 
his meaning, in order to carry on the contest with greater 
advantage ; or to impute to him consequences which we 
imagine may be derived from his doctrine, although he 
disavows and denies them. All this may be reduced to 
this kind of sophism, which an honest and good man ought 
to avoid above all things." 

Logicians have distinguished and described certain kinds 
of argument which are valid, and may fairly enough be 
used, provided that it is clearly seen and admitted that they 
have no bearing upon the main question. The Fallacy 
consists in referring such arguments to a wrong Conclusion, 
in urging them as if they established the real point of con- 
troversy, whereas they actually tend only to direct censure 
or laughter against those who hold the opposite opinion, or 



800 OF FALLACIES. 

to some other equally irrelevant object. Let the reasoning 
which tends directly to prove the main point at issue be 
called the argumentum ad rem. Then the argumentum ad 
hominem is that which convicts your opponent of inconsis- 
tency, ignorance, bad faith, or illogical reasoning. Any or 
all these charges may be well founded, but they are aside 
from the purpose ; for the doctrine which is in dispute may 
be well founded, though its supporter is deficient in all the 
qualities of a good reasoner. The argumentum ad vere- 
cundiam appeals to our reverence for some high authority, 
or some venerable institution, as a means of silencing an 
opponent, but not of convincing him that he is mistaken 
in opinion. The argumentum ad populum is a similar 
appeal to the passions or prejudices of common people ; it 
is a fair inference that proper arguments are wanting, when 
such appeals are permitted. 

To these must be added the argumentum ad ignorantiam, 
which is asserting that your own position is correct, unless 
your opponent can show some valid reason to the con- 
trary. This mistake is often committed with reference to 
alleged occurrences which appear to us strange and improb- 
able, or which we may even believe to be impossible. The 
Fallacy consists in denying that the thing is so, merely be- 
cause we do not know how it is so. But if this reasoning 
were correct, we ought to deny that the human will has 
any control over a single movement of our animal organ- 
ism, or even that the grass grows ; for, certainly, no one 
can tell how a mere volition moves the arm, or how the 
green herb in the spring-time absorbs inorganic matter and 
assimilates it to itself. But our ignorance of one thing, the 
modus operandi, is no disproof of a very different thing, the 
opus operatum. The king of Siam was illogical in denying 
that water could become ice, merely because, within his 
experience, a liquid had never become solid. The incon- 
ceivable is no sure indication of the impossible. Sir Wil- 



OF FALLACIES. 301 

liam Hamilton even undertakes to show, that all which is 
conceivable in thought lies between two extremes, both of 
which are inconceivable, but of which, as they are contra- 
dictories of each other, one must be true. 

But lest this exposition should seem to favor credulity 
and superstition, it should be observed, that the paralogism 
here exposed is usually met by a counter argument just as 
untenable as the one which it is brought forward to con- 
fute. Because neither I nor you know hoio a certain 
phenomenon is produced, I am not justified in arbitrarily 
assigning it to a certain cause, whether natural or super- 
natural, and then calling upon you to accept this explana- 
tion for want of a better. This also would be an appeal 
to ignorance, — an attempt to found knowledge upon ig- 
norance. To take an mstance from the reputed wonders 
of animal magnetism ; — perhaps I do not know Jiow the 
table tips ; but you are not therefore to assume that spirits 
from the other world are tipping it. It is an ignoratio 
elenchi to argue, that your hypothesis must be well founded 
because I am not able to invent a better. Your business 
is to support your own Conclusion by valid reasoning, not 
to rest it merely on my inability to prove the opposite. 

This Fallacy pervades all tlie speculations of those whom 
Dr. Whewell calls the uniformitarian school of seolocrists. 
They argue that the geological phenomena now visible, 
many of which are of stupendous magnitude, can be ac- 
counted for by the ordinary working of physical causes 
now in operation, if we only assign a sufficient lapse of time 
for the cumulation of their results. It is unnecessary, they 
say, to suppose that there was any cataclasm, any violent 
disruption of what is the usual course of nature in our own 
days, in order to account for the elevation of vast mountain 
chains, the sinking of continents, or the dislocation of strata 
many miles in thickness ; the same causes, which are now 
altering; the level of a continent at the rate of an inch in a 



302 OF FALLACIES. 

century, can have piled up the Andes or the Himalayas, if 
you give them time enough. Perhaps so ; and yet it may 
be questioned which is the more violent supposition, the 
sudden and irresistible outbreak of a power whose opera- 
tions, at least on so grand a scale, have never since been 
witnessed, or the undisturbed lapse of those countless mil- 
lions of ages on which the imaginations of geologists love to 
dwell. But this is not the real question. Their ignoratio 
elenchi consists in multiplying proofs that slow-working 
causes might have effected all these stupendous results, 
and then jumping at the Conclusion that these causes 
did so produce them. They propound this Dilemma : — 
Accept this solution of the problem, or propose a better 
one. We may logically dechne to do either. An ingeni- 
ous mechanic, witnessing for the first time the uniform 
motion of the hands over the dial-plate of a clock, if chal- 
lenged to explain, without inspecting the works, how this 
equable and long-continued motion could be produced, 
might easily invent a combination of springs, wheels, and 
pinions, which would be adequate for the purpose ; but it 
would be extravagant for him to assume that the machin- 
ery thus invented by himself was an exact copy of the 
works which he had not been allowed to examine. He 
could only say, the results in question might he brought 
about by my apparatus ; but I cannot tell how they are 
actually produced. Science does not rest on hypothesis, 
and is not content with possible explanations of phenomena. 
The well-known rule in controversy, that the burden of 
proof rests on him who maintains the affirmative, because 
it is difficult, or impossible, to prove a negative, rests on 
the considerations here alleged. In order to prove a nega- 
tive, it must be demonstrated that not one out of many 
different contingencies admits the positive. Thus a survey 
of the whole field is necessaiy, and the exclusion of the 
opposite hypothesis from every point in it must be made 



OF FALLACIES. 303 

certain. On the other hand, the proof of the positive is 
estabhshed at a single point ; no wide range of search is 
requisite. To borrow an illustration, it is easy to demon- 
strate that the book is in the room ; we have only to pro- 
duce it. But to prove that it is not there, " it must be 
made certain, first, that every book in the room has been 
found and examined, secondly, that it has been correctly 
examined. No one, in fact, can prove more than that he 
cannot find the book ; whether the book be there or not, is 
another question, to be settled by our opinion of the vigi- 
lance and competency of the searcher." The geologists 
say their opponents cannot find any proof that the ordinary 
working of Nature's laws could not, in an indefinite lapse 
of years, produce the effects in question. What is that to 
the purpose ? Our inability to find a needle in a hay-mow 
is no proof that the needle is not there. 

Indirectly, indeed, many negatives are established by a 
single positive ; it is thus that an accused person in court 
makes a triumphant defence by proving Avhat the lawyers 
call an alibi ; direct testimony that he was in Manchester, 
on the night in question, is an indirect demonstration that 
he was not in any part of Birmingham, where the crime 
must have been committed. Here, the testimony required 
is positive in character, though it tends indirectly to a nega- 
tive result ; hence, it is easily obtained. Sometimes, in- 
deed, when there are but few possible cases, so that the 
field for search is very limited, we may be required to 
prove a negative directly. This is the nature of the ge- 
ometer's demonstration per impossibile, as it is called. Fail- 
ing to obtain direct proof that the angle A is equal to the 
angle B, we remember that only three suppositions are pos- 
sible ; and then, by demonstrating that it cannot be either 
greater or less, we indirectly prove tliat it must be equal. 
In hke manner, after it has been proved that the accused 
person committed a homicide, it is a presumption in law 



304 OF FALLACIES. 

that the act was done " with malice prepense " ; in other 
words, the law puts upon the accused the ■ burden of proof 
that he did not do it maliciously. But this seemingly harsh 
presumption of law rests, as Mr. De Morgan remarks, upon 
the fact, that there are so few alternatives to the supposi- 
tion of wilful murder ; in order to disprove malice, the 
accused is only required to make out either mishap, insan- 
ity, or heat of blood. He is not put to hunting for a needle 
in a hay-mow, under penalty of being hanged if he fails ; 
but, out of four possible cases, he is obliged to disprove the 
single fatal supposition by direct evidence that his case is 
some one of the three others. 

Most rhetorical artifices may be referred to the class of 
the ignoratio elenchi. Thus, says Dr. Whately, " when 
the occasion or object in question is not such as calls for, or 
as is likely to excite in those particular readers or hearers, 
the emotions required, it is a common rhetorical artifice to 
turn their attention to some object which will call forth 
these feelings ; and when they are too much excited to be 
capable of judging calmly, it will not be difficult to turn 
their passions, once roused, in the direction required, and 
to make them view the case before them in a very different 
light. When the metal is heated, it may easily be moulded 
into the desired form. Thus, vehement indignation against 
some crime may be directed against a person who has not 
been proved guilty of it; and vague declamations against 
corruption, oppression, &c., or against the mischiefs of 
anarchy, with high-flown panegyrics on liberty, rights of 
man, &c., or on social order, justice, the constitution, law, 
religion, &c., will gradually lead the hearers to take for 
granted, without proof, that the measure proposed will lead 
to these evils, or to these advantages ; and it will in con- 
sequence become the object of groundless abhorrence or 
admiration." 

Under this class of fallacies also mny be ranked the 



OF FALLACIES. 305 

error of adopting an argument which proves either too little 
or too much. In one of these cases, however, the error is 
by no means so serious as in the other. The reasoning 
which proves too Httle may be good as far as it goes ; it 
conduces to the end in view, and, taken in conjunction 
with another argument also partial in its effect, it may 
establish the whole doctrine in question. But the argu- 
ment which proves too much is invalid throughout ; Fahus 
in uno, fahus in omnibus, is a sound logical maxim. If 
any portion of the Conclusion is evidently false, the rea- 
soning which led to it, considered in itself alone, must 
be essentially and altogether vicious ; since fi'om correct 
premises, and by valid inference, no error whatever can 
possibly be deduced. 

When the main purpose is to disprove a pai'ticular doc- 
trine, it is not enough to refute one or more aro-uments 
that have been alleged in its support ; this is merely con- 
futing your opponent, and not the proposition which he 
maintains, and which may be supported by better reasons 
than he has been able to adduce. In like manner, to state 
objections, though they may be perfectly valid ones, to a 
specific plan of action, is insufficient to prove that this plan 
ought to be rejected ; for it may well be that some action 
is unavoidable, and yet that strong objections may be urged 
against every mode of action that can be devised. When 
the Necessitarian says that the doctrine of the freedom of 
the human will is inconceivable. Sir William Hamilton 
justly replies, that the argument proves too little ; for it is 
at least equally inconceivable that the will should not be 
free. Unbelievers, says Dr. Whately, " may find numer- 
ous objections against various parts of Scripture, to some 
of which no satisfactory answer can be given ; and the 
incautious hearer is apt, while his attention is fixed on 
these, to forget that there ai'e infinitely more and stronger 
objections against the supposition that the Christian religion 



306 OF FALLACIES. 

is of human origin ; and that, where we cannot answer all 
objections, we are bound in reason and in candor to adopt 
the hypothesis which labors under the least." 

3. A full illustration of the FaDacy, non causa pro causa, 
would carry us too far into the domain of the physical 
sciences, and therefore would be more in place as a chapter 
of Applied Logic. Only the more frequent and obvious 
errors of this class can be noticed here. Prominent among 
these are the common blunders of reasoning post lioc, ergo 
propter hoc; of mistaking physical laws for efficient causes ; 
and of applying the doctrine of the Necessitarian or Fatalist 
as a motive of action, or rather of inaction, in our ordinary 
concerns. 

An invariable antecedent is a sign, but often it is indis- 
putably not a cause, of the phenomenon which it precedes. 
As that which leads the mind to expect a certain event, it 
may be regarded as a causa cognoscendi ; but this is very 
different from the causa essendi, which is the ordinary sig- 
nification of the word cause. Cicero states this distinction 
very clearly : — Causa autem ea est quce id efficit cujus est 
causa. Non sic causa intelligi debet, ut, quod cuique ante- 
cedat, id ei causa sit, sed quod cuique efficienter anteeedat. 
In this sense, deliberation is certainly not the cause of the 
action which follows it, nor is one beat of the pulse the 
cause of the subsequent beats. In fact, two successive 
states of the same substance are seldom regarded even by 
the vulgar as cause and effect. But since we necessarily 
think a cause as immediately preceding its effect, or as 
simultaneous with it, the mind is prone, especially in the 
case of obscure and anomalous phenomena, of which the 
true cause cannot easily be discovered, to consider any an- 
tecedent event as such a cause. This is the origin of the 
belief in omens, and many other superstitions of the Vulgar. 
An accidental conjunction in time between some private 
or public calamity, and the appearance of a meteor or a 



OF FALLACIES. 307 

comet, or the occurrence of an earth pake, is regarded as 
indicating a causal union of the two events. The science 
of medicine, at least in that branch of it which is called 
therapeutics, is little else than an application of the maxim. 
Post hoc, ergo propter hoc. The Avisest physician cannot 
tell, m any one case, whether the recovery of the patient 
took place because he swallowed the drugs, or in spite of 
them, or whether they were powerless in respect either to 
good or evil. A harsh application of this fallacious rule 
consists in judging the wisdom of a man's conduct by its 
consequences, or the uprightness of his intentions by the 
immediate results of his action upon the happiness or 
misery of those around him. A brave and able com- 
mander is not always successful in battle, and a consci- 
entious and kind-hearted man may be compelled by a 
sense of duty to inflict suffering and death. Practical 
men, as they are called, who profess to be guided only by 
experience, and to rely upon facts instead of theories, are 
especially liable to this class of errors. In their eyes, the 
disorders and other evils which follow some long-delayed 
reform are attributable to the reform itself, and not to its 
xmdue postponement. 

Forming an induction fi'om too small a class of cases, 
and disregarding negative instances, are the frequent 
source of this confusion between an antecedent phenome- 
non and an efficient cause. The most common of all the 
superstitions of the vulgar, the belief that Friday is an 
unlucky day for beginning any new enterprise, may be 
traced to this origin. And it should not be forgotten, that 
the prognostications of evil thus formed very often bring 
about their own fulfilment ; fearful and dispirited men 
can make little effectual effort to avert danger. The 
belief in the hereditary transmission of diseases of mind 
and body, at least in the unreasonable extent to which it 
new prevails, is formed in this manner, and tends in this 



308 OF FALLACIES. 

way to verify itself. Gout and insanity run in families 
where a perpetual apprehension of them exists, and where, 
perchance, habits of life are actually transmitted fi'om 
father to son which are likely to induce and foster such 
diseases. But even in these cases, a careful enumeration 
might satisfy one that, of all who are within the unlucky 
circle, at least as many escape the dreaded calamity as 
those who suffer from it. Were it otherwise, indeed, the 
circle would continue to enlarge itself in successive gener- 
ations, till few could hope to escape the hereditary taint. 
As Dr. Johnson remarks, the one prophetic dream which 
comes to pass is remembered and spoken of, while the 
ninety and nine which fail of accomplishment are for- 
gotten. 

" In mmds not habituated to accurate thinking," says 
Mr. Mill, " there is often a confused notion that the gen- 
eral laws are the causes of the partial ones ; that the law 
of general gravitation, for example, causes the phenomenon 
of the fall of bodies to the earth. But to assert this would 
be a misuse of the word cause; terrestrial gravity is not 
an effect of general gravitation, but a case of it ; that is, 
one kind of the particular instances in which that general 
law obtains." A Law of Nature is only a general fact, or, 
rather, a general statement comprehending under it many 
similar individual facts. Hence, such a Law does not ac- 
count for^ or explain^ the phenomena of Nature ; it only 
describes them. Thus, it is not a Law of Hydrostatics 
which causes water to remain at the same level in the two 
arms of a bent tube ; but the fact that water stands at this 
level is ranked among many other facts, which are com- 
prehended under the general statement called a Law of 
Hydrostatics. 

The process of Thought by which Ave pass from a Phys- 
ical Law to an individual case happening under it is one 
of Deduction, and is therefore governed by the dictum de 



OF FALLACIES. 309 

omni. Because all bodies tend to fall towards the common 
centre of gravity, therefore this body thus tends to fall. 
Hence, the statement of the Law is that which makes us 
believe that the individual event will happen ; and this, by 
a very natural confusion of Thought, is mistaken for the 
cause which makes the event happen. But the relation in 
the former case is that between Premises and Conclusion ; 
in the latter, between Cause and Effect ; the former is a 
law of Thought, the latter is a law of things ; the one is 
the causa cognoscendi, the other, the causa essendi. 

The Fallacy here exposed is one of much interest, as it 
is that which lies at the bottom of every scheme of Materi- 
alism, — every attempt to account for the origin of species, 
and the general phenomena of the universe, without bring- 
ing in any other agency than that of mere Physical Laws, 
or what it was once the fashion to call " Second Causes." 
Such a theory is not only insufficient, or unsupported by 
the requisite evidence ; it is founded upon a mere confusion 
of Thought, and is illogical and absurd. There is no such 
thing as the agency or action of a Law ; except as a figure 
of speech, we might as well predicate locomotion of an idea^ 
or speak of bilateral triangles. " Second Causes " are no 
causes at all ; they are mere fictions of the intellect, and 
exist only in Thought. A cause in the proper sense of the 
word, that is, an efficient cause, as original and direct in its 
action, must be a First cause ; that through which its ac- 
tion is transmitted is not a cause, but a portion of the 
effect^ — as it does not act, but is acted upon. 

The Ignava Matio, or do-nothing argument, is a falla- 
cious application of the Necessitarian theory. According 
to this theory, all occurrences whatever have their environ- 
ment of circumstances, with which they stand in neces- 
sary and fixed relations by an absolute law ; and the state 
of the universe at any one moment, in all its parts, from 
the creation of a world to the stirring of an aspen-leaf, could 



310 OF FALLACIES. 

not possibly have been different from what is. Every oc- 
currence has its cause, of which it is the necessary result^ 
and to which it is necessarily proportioned, even in the 
mmutest respects. Every event, of course, is surrounded 
by other events, and must be considered as being at the 
same t»me both antecedent and consequent, — as necessa- 
rily resulting from those which preceded it, and neces- 
sarily followed by those which come after it, — and thus 
as forming one link in an adamantine chain which extends 
from eternity to eternity. As Mr. Mill himself, an en- 
lightened and consistent advocate of this theory, remarks, 
" there is no Thing produced, no event happening, in the 
known universe, which is not connected by a uniformity, 
or invariable sequence, with some one or more of the 
phenomena which preceded it ; insomuch that it will hap- 
pen again as often as these phenomena occur again, and 
as no other phenomenon having the character of a counter- 
acting cause shall coexist. These antecedent phenomena, 
again, were connected in a similar manner with some that 
preceded them ; and so on, until we reach, as the ultimate 
step attainable by us, either the properties of some one 
primeval cause, or the conjunction of several. The state 
of the whole universe at any instant we believe to be the 
consequent of its state at the previous instant; insomuch 
that one who knew all the agents which exist at the pres- 
ent moment, their collocation in space, and their properties, 
— in other words, the laws of their agency, — could pre- 
dict the whole subsequent history of the universe, at least 
unless some new volition of a power capable of controlling 
the universe should supervene."* 

The confutation of this astounding theory is tl. 3 business 
of the metaphysician or the theologian ; we have no con- 
cern with it here, except to point out the Fallacy of re- 
garding it as justifymg inaction, or as demonstrating the 

* Mill's Logic, 3d ed., Vol. I. p. 358. 



OF FALLACIES. 311 

hopelessness of any endeavor on our part to control the 
:ourse of natural events. The Ignava Rath is thus stated 
by Cicero, in the form of an argument against taking any 
measures for the restoration of one's health. 

If it is fated that you shall recover from the present disease, then 
you will recover whether you call in a physician or not. 
If it is fated that you shall not recover, then, with or with- 
out a physician, you will not recover. 

But either the one or the otlier of these two contradictories is 
fated. 

Therefore, it will be of no use to call in a doctor. 

As Cicero remarks, if this reasoning were correct, our 
whole life would be reduced to a state of hopeless inactiv- 
ity ; as it would prove the inutility of any endeavor to 
bring about a desirable result, or to avert a threatened 
calamity. The Turks, who are fatalists, so understand it, 
and reduce it to practice by refusing to take any precau- 
tions against a pestilence, or to remove a lighted match 
from its dangerous proximity to a powder-magazine. But 
they only show thereby that they are incapable of follow- 
ing out correctly the logical consequences of their own doc- 
trine. Calling in medical aid furnishes a new antecedent, 
and thus presents a new case for the determination of Fate. 
It may also be fated that I should send for a physician, and, 
with his aid, that I should recover ; or it may be fated that 
he should not be called in, and, as a consequence of this 
neglect, and not as a necessary result of the disease alone, 
that I should die. Fate is only a concurrence of causes 
and an assemblage of conditions ; supply a new cause, take 
away one of the necessary conditions, and the result will 
be differc.nt, though it will still be a fated or necessary 
result. Zeno aptly conftited this Fallacy, when he was 
whipping a slave, who called out, in excuse for his fault, 
that it was fated for him to steal ; " And so it is for me to 
whip you," was the reply. 



312 OF FALLACIES. 

Most of the sophisms once called Inexplicable have been 
already resolved in treating of the different classes of Fal- 
lacies to which they were respectively referred. It is only 
necessary to consider here the famous argument, called the 
Achilles, proposed by Zeno the Eleatic, as Mr. Mansel says, 
" to support the leading tenet of Parmenides, of the unity 
of all things, by showing that the identity of rest and mo- 
tion is a necessary result from the contrary opinion." It 
might more aptly be adduced to prove that extension is not 
infinitely divisible, for if it were so, according to this argu- 
ment, motion would be impossible. The sophism is thus 
stated. 

The swiftest runner can never overtake the slowest, if 
the latter has ever so little the start. Suppose, for instance, 
that Achilles runs ten times as fast as a tortoise, and that 
the tortoise is one mile in advance at the outset. While 
Achilles is traversing this mile, the tortoise has advanced 
Y^Q th of a mile farther ; before his pursuer has passed over 
this YQ^th, the tortoise has advanced y^Q-th, and then, again, 
YoVo^th, and so on forever, always being some fraction, 
however small, of a mile in advance. 

Dr. Whately seems to have been entirely puzzled by 
this sophism, as he does not attempt a solution of it, but 
merely remarks that it " furnishes a confirmation of the 
utility of an acquaintance with the Syllogistic form, in 
which form the pretended demonstration cannot possibly 
be expressed." But this confession, as Mr. Mansel ob- 
serves, " is in fact a surrender of the Syllogistic criterion, 
as a means of discriminating between sound and ninsound 
reasoning. On the contrary, nothing is easier than to ex- 
hibit the reasoning in a Syllogism, and to show thereby 
that the fallacy does not lie in the Form, but the Matter. 
Thus, representing the whole space to be traversed by a, 

'Any space equal to j^ + ^ + -~^, &c. is infinite (being the 
sum of an infinite series). 



OF FALLACIES. * 313 

' The space to be passed before Achilles overtakes the tortoise is 

equal to this sura. 
' Therefore, it is infinite.' 

" The whole logical mystery of this famous Fallacy lies 
in this, that the major premise is false. The sum of an 
infinite series may be, and in this case is, finite. This 
premise is equally false, whether space is, or is not, divis- 
ible ad infinitum.^' * 

Fries remarks that the sophistry is here covered up by 
the mode of stating the problem. The question really 
asked is, when will Achilles have passed over the particular 
extent of ground which the tortoise, at any one moment, has 
already left behind him; and this question, on account of 
the infinite divisibility of space and time, may be repeated 
ad infinitum. The true question, at what point will Achil- 
les overtake the tortoise, is not allowed to come into view. 
The space between the two parties, however small, is, in 
thought, though not in reality, infinitely divisible ; and the 
series of constantly diminishing terms into which it is 
mentally broken up, thovigh infinite in number, is finite in 
amount, the sum of the series being equal, of course, only 
to the small space originally divided. Any finite quantity 
may be broken up into an infinite number of terms, if these 
terms become infinitely small. The confusion of thought 
consists in mistakino; the sum of the terms of such a de- 
scending series, composed of infinitesimals, for the sum of 
an infinite series the terms of which are not infinitely small. 
It is only this latter sum which is necessarily an infinite 
quantity. 

* Hansel's Notes to Aldrich, pp. 141, 142. 



14 



314 • APPLIED LOGIC. 



CHAPTER X. 



APPLIED LOGIC. 



APPLIED Logic, as it will be here understood, includes 
both what has usually been called the Doctrine of 
Method, and what Sir William Hamilton terms Modified 
Logic. Its object is the proper regulation of the Thinking 
Faculty, not only in forming individual cognitions, but in 
the more complex processes required for the construction 
and advancement of Science. Pure Logic, as we have 
seen, is concerned only with the Forms of Thought ; it 
considers these as given, or already formed, and regards 
only the necessary and fundamental laws, emanating from 
the" mind itself, which have concurred in their formation 
and wliich regulate their use. Applied Logic has regard 
also to the Matter of Thought, — to the infinitely numer- 
ous and diversified objects of cognition which Nature fur- 
nishes us, — and considers by what general processes these 
are brought within the grasp of mind, or are made intelli- 
gible, or, what is the same thing, are put under the Forms 
of Thought. The laws which govern these processes are 
not universal and necessary, as in the former case, but are 
contingent and varied, depending, in part, on the diverse 
and multiform characteristics of the objects of cognition, 
and, in pai't, on the powers and limitations of the hmnan 
mind itself. To avoid the vagueness and perplexity which 
result from attempting to grasp too much, Applied Logic 
treats directly only of the latter, — that is, of the formation 
of Science so far as this depends on tlie nature of the human 



APPLIED LOGIC. 315 

intellect, leaving to the special sciences the duty of adapt- 
ing their own procedures to the nature of the peculiar 
objects of study with which they are immediately con- 
cerned. 

This division, however, like many others in Science, can- 
not be always accurately preserved. The processes through 
which the mind acts can be exemplified only in their appli- 
cation to various classes of objects, and as varying some- 
what with the nature of those objects. The practical dis- 
tinction will be, that Applied Logic regards the peculiarities 
of what we are thinking about only so far as these illusti'ate, 
and in some measure direct, the processes of thinking. It 
considers primarily how the mind acts, and only secondarily 
what it is acting upon. 

Science is a body of truths relating to any well-defined 
object or class of objects, so arranged as to be easily com- 
prehended and retained, and conveniently used. The mer- 
its at which it aims are Completeness, Thoroughness, and 
Method. Its objects are the numberless things which Na- 
tm'e furnishes us for study. 

What we call Nature is an assemblage of objects and a 
succession of events. The mind, on account of the limita- 
tion of its faculties, and the endless number and vaiiety of 
these objects and events, cannot grasp and consider them 
all at once. Neither can it undertake to study successively 
each individual thing by itself; for a lifetime might be so 
spent, before we could obtain even a small fraction of the 
knowledge which is requisite for the proper guidance of life. 
The first necessity, then, which is imposed upon us by the 
constitution of the mind itself, is to break up the infinite 
wealth of Nature into groups and classes of things, with 
reference to their resemblances and afiinities, and thus to 
enlarge the grasp of our mental faculties, even at the ex- 
pense of sacrificing the minuteness of information which 
can be acquired only by studying objects in detail. The 



316 APPLIED LOGIC. 

first efforts in the pursuit of knowledge, then, must be 
directed to the business of Classification. Perhaps it will 
be found in the sequel, that Classification is not only the 
beginning, but the culmination and the end, of human 
knowledge. 

We will first consider the mental processes through which 
we gain a knowledge of real Objects, — that is, of Objects 
which coexist in space, leaving for subsequent inquiry the 
question, how far these processes must be modified in con- 
structing a science of Events which succeed each other in 
time. 

It has already been remarked, that the beginning of all 
knowledge is in single acts of the Perceptive or Acquisitive 
Faculty, which operates either through the external senses, 
thus constituting External Perception, or through that no- 
tice which the mind takes of what is passing within itself, 
this being denominated Consciousness, or Internal Percep- 
tion. In either case, one indivisible act of the Perceptive 
Faculty gives us to know only one phenomenon. A suc- 
cession of such acts relating to one Object fiirnishes a num- 
ber of cognitions of the qualities or attributes of that Ob- 
ject; and these qualities we unite together, and bind up 
into one whole, through the conception, which the mind 
furnishes, of Substance, or that in which the qualities inhere. 
Thus, suppose the Object presented is an apple ; the eye 
tells me that it is red; the touch, that it is spherical and 
moderately hard ; the muscular sense, that it has weight ; 
the taste, that it is subacid, &c. ; and these qualities I unite 
into one whole by the conception of one substance in which 
they all inhere, and call the aggregate thus formed apple. 
The reason why just these qualities, and no others, are 
united into the whole is, that tliey all are, or may be, 
received at one time, under the same circumstances, and 
appear to proceed fi'om one Object, as they are referred by 
me to one definite locality in space. 



APPLIED LOGIC. 317 

Take another instance from Internal Perception. I am 
conscious, either at once or in succession, of joy or pain, of 
a thought, reminiscence, or vohtion, of a sensation of hun- 
ger, coldness, &c. ; and these separate Intuitions I put 
together into one whole through the Intuition, which enters 
into each of them, that they are mine^ or that they all be- 
long to the one person which I call myself. Here, the Intui- 
tion of Self is the unifying principle, or that through which 
the aggregation of many into one is accomplished, just as, 
in the fonner case, it was the conception of Substance. 

Manifestly, then, the first step towards the formation of 
science is a S^Tithesis, a putting together of the Matter of 
several Intuitions into that one whole which we call an 
Individual Object. This Object itself, though called an In- 
dividual, as if it were one thing, has in truth only a virtual 
unity ; it is really complex, consisting of many parts and 
many qualities, which were at first separately perceived ; 
but having often been perceived together, or in combina- 
tion, they become so firmly united that the perception of a 
few, perhaps of only one, of its parts or qualities immedi- 
ately calls up the imagination of all the others, that is, of 
the whole. Thus, I am said to perceive the apple, when, 
in fact, I perceive only its shape and color ; but this shape 
and color immediately suggest all its other qualities, and 
the complex Intuition thus formed, partly perceived and 
partly imagined, is what is called, though improperly, a 
single perception of one thing. The wholes thus formed 
are of all degrees of complexity, either having as many 
parts, qualities, and uses as a house or an intricate machine, 
or as fcAv as a spot of pui-ple cloud in the sky. They may 
be either real or factitious, the conception and belief of 
actual existence being one of the parts or elements of the 
former, but not of the latter. Each of these wholes is, or 
might be, designated by a Proper Name, belonging to this 
one thing and to nothing else. 



318 APPLIED LOGIC. 

But as the number of such Objects and Names would be 
endless, we seek, as has been said, to bnng them within 
the grasp of the mind by throwing them into groups and 
classes. The first step of the process directed to this end 
is the reverse of the former one ; we must now begin by 
Analysis. The many complex wholes, called Individual 
Objects, which we have previously formed by a procedure 
so easy and so frequently repeated that we are almost un- 
conscious of it, must now be resolved into their constituent 
parts and properties, in order that, by an abstraction of 
their dissimilar elements and restricting; the attention to 
those which are similar, classes may be formed, all the 
members of which have some like or equivalent attributes. 
The process of Classification, then, is an Analysis immedi- 
ately followed by a Synthesis into groups, this Synthesis 
being directed by the Comparative or Elaborative Faculty 
of the mind, the chief function of which is the perception 
of relations, and especially the relations of likeness and 
unlikeness. Having formed one set of classes, called the 
Infimse Species, because they are composed of Individuals 
only, we then proceed, in an exactly similar way, to group 
these groups into Genera ; and so on, erecting a hierarchy 
of Concepts, until we at least approximate a Summum 
Genus, or that thought which embraces all conceivable 
things. The highest generalization usually attempted is 
that which arranges all existence, whether actual or poten- 
tial, under the three heads, Man, the Universe, and God 
who is Absolute Being and Absolute Cause. 

Evidently, then, the universal procedure of Science is 
an Analysis followed by a Synthesis, the result of the 
whole being a more or less complete Classification. All 
the problems which Science has to solve may be reduced 
to these two questions : What Classes ought to be formed ? 
and, Does this or that Object possess the special attribute or 
attributes which entitle it to be ranked under a certain 



APPLIED LOGIC. 319 

Class ? Isolated cognitions — the knowledge, for instance, 
that this particular attribute does, or does not, belong to 
this particular thing — are not entitled to be called Sci- 
ence, until they are arranged in some Class, or subsumed 
under some comprehensive Law. 

There is a confusion in the application of the terms Anal- 
ysis and Synthesis, which may be best resolved by bor- 
rowing a passage from Sir Wilham Hamilton. " It is 
manifest, in general, from the meaning of the words, that 
the term Analysis can only be applied to the separation of 
a whole into its parts ; and that the term Synthesis can 
only be applied to the collection of parts into a whole. So 
far, no ambiguity is possible, — no room is left for abuse. 
But there are different kinds of whole and parts ; some of 
the wholes, like the whole of Comprehension (called also 
the MetaphydcaV), and the whole of Extension (called also 
the Logical), are in the inverse ratio of each other; so 
that what in the one is a part, is necessarily in the other a 
whole. It is evident, then, that the counter processes of 
Analysis and Synthesis, as applied to these counter wholes 
and parts, should fall into one, or correspond ; inasmuch as 
each in the one quantity should be diametrically opposite to 
itself m the other. Thus, Analysis, as applied to Compre- 
hension, is the reverse process of Analysis as applied to 
Extension, but a corresponding process with Synthesis ; 
and vice versa. Now, should it happen that the existence 
and opposition of the two quantities are not considered, — 
that men, viewing the whole of Extension or the whole of 
Comprehension, each to the exclusion of the other, must 
define Analysis and Synthesis with reference to that sin- 
gle quantity which they exclusively take into account ; — 
on this supposition, I say, it is manifest that, if different 
philosophers regard different wholes or quantities, we may 
have the terms Analysis and Synthesis absolutely used by 
different philosophers in a contrary or reverse sense. And 



320 APPLIED LOGIC. 

this lias actually happened. The ancients, in general, 
looking only to the whole of Extension, use the terms 
Analysis and Synthesis simply to denote a division of the 
Genus into Species, — of the Species into Individuals ; the 
moderns, on the other hand, in general, looking only at the 
Avhole of Comprehension, employ these terms to express a 
resolution of the Individual into its various attributes." 

The words analytic and synthetic^ Hamilton further ob- 
serves, " are, lilie most of our logical terms, taken from 
Geometry " ; and the applications of them in this science 
are thus admirably illustrated by Dr. W he well. In discur- 
sive processes of reasoning, he remarks, " we obtain our 
conclusions, not by looking at our conceptions steadily 
in one view, which is intuition^ but by passing from one 
view to another, like those who run from place to place 
Qdiscursus^. Thus, a straight line may be, at the same 
time, a side of a triangle and a radius of a circle ; and in 
the first proposition of Euchd, a line is considered first in 
one of these relations, and then in the other, and thus the 
sides of a certain triangle are proved to be equal. And by 
this ' discourse of reason,' as by our older writers it was 
termed, we set forth from those axioms which we perceive 
by intuition, travel securely over a vast and varied region, 
and become possessed of a copious store of mathematical 
truths." In such geometrical reasoning, he continues, " we 
introduce at every step some new consideration ; and it is 
by combining all these considerations that we arrive at the 
conclusion, that is, the demonstration of the proposition. 
Each step tends to the final result, by exhibiting some part 
of the figur'e under a new relation. To Avhat we have 
already proved, is added something more ; and hence this 
process is called Synthesis, or putting together. The proof 
flows on, receiving at every turn new contributions from 
difixirent quarters ; like a river fed and augmented by 
many tributary streams. And each of these tributaries 



APPLIED LOGIC. 321 

flows from some definition or axiom as its fountain, or is 
itself fonned by the union of smaller rivulets which have 
sources of tliis kind. In descending along its course, the 
synthetical proof gathers all these accessions into one com- 
mon trunk, the proposition finally proved. 

" But we may pi'oceed in a different manner. We may 
begin from the formed river, and ascend to its sources. 
We may take the proposition of which we require a proof, 
and may examine Avhat the supposition of its truth implies. 
If this be true, then something else may be seen to be 
true ; and from this, something else, and so on. We may 
often, in this way, discover of what simpler propositions our 
theorem or solution is compounded, and may resolve these 
in succession, till we come to some proposition which is 
obvious. This is geometrical Analysis. Having succeeded 
in this analytical process, we may invert it ; and may de- 
scend again, from the simple and known propositions, to the 
proof of a theorem, or the solution of a problem, which was 
our starting-place." * 

We have said that an Individual Object, as thought, is a 
Synthesis of parts and attributes. But it is not an arbi- 
trary Synthesis, — not a putting together of any elements 
whatever, such as mere caprice may have induced us to 
select. Imaginary Objects, it is time, may be thus built up 
at pleasure ; mere fancy may construct a centaur, a griffin, 
or any other imaginative creation, recognizing it at the mo- 
ment to be unreal. But if actual existence is one of the 
elements of the combination, that is, if the Object thus 
thought is understood to be a real Object, our conception of 
it must be a Synthesis of such parts and properties only as 
we know it actually possesses. Truth may be defined to 
be tiie conformity of our mental representations to the 
things which they are intended to represent ; and in Ap- 
plied Logic, where we are concerned not only with the 

* Philosophij oftlie Inductive Sciences, Vol. I. p. 144. 
14* U 



822 APPLIED LOGIC, 

Form, but with the Matter, of Thought, truth is the chief 
object in view, — the first requisite of Science. The Syn- 
thesis in thought is true only when it corresponds to the 
combination which exists in nature. 

In Hke manner, the Classification which is to serve the 
purposes of Science cannot be arbitrary. In the construc- 
tion of Science, the first, and perhaps the most difficult, 
question which we have to answer is. What classes ought 
to be formed. " The power of framing classes," says Mr. 
Mill, " is unlimited, as long as there is any (even the 
smallest) difference to found a distinction upon. Take 
any attribute whatever, and if some things have it and 
others have it not, we may ground upon this attribute a 
division of all things into two classes ; and we actually do 
so, the moment we create a name which connotes the 
attribute " ; — as the class of white things, and that of 
things not-white. " The number of possible classes, there- 
fore, is boundless ; and there are as many actual classes 
(either of real or imaginary things) as there are general 
names, positive and negative together." 

The relations and connections of the various attributes 
with each other must guide us in selecting those upon 
which the Classification is to be founded. The purpose of 
the arrangement is, that all the individual objects included 
in any one class shall have as many common or similar 
elements as possible ; — that they shall resemble each other 
in numerous and important respects. Now it is found that 
certain attributes always carry along with them, or are 
constantly found in company with, many other attributes ; 
— not merely those which are necessarily thus connected 
as derivative from them by necessary mference, but many 
others, of which we can only say that nature ahvays puts 
them together. On the other hand, certain attributes 
have no such regular companionship, but are found indif- 
ferently in connection with entirely different sets of ele- 



APPLIED LOGIC. 323 

merits. Among inorganic bodies, for example, tlie metallic 
property is an instance of the former class ; among animals, 
the possession of a vertebrated column or backbone. There 
is good reason, then, for forming a class of Metals, and a 
class of Vertebrates, because we are vsure that each of these 
classes will have many common properties, besides the sin- 
gle one from which their name is derived. On the con- 
trary, the same color or the same magnitude is not found in 
constant companionship with many other qualities, so that 
it would be comparatively useless to form a class of white 
objects, or a class of animals three feet high. Such classes 
would be found to include the most dissimilar and hetero- 
geneous members. 

It is evident even from these few examples, that the 
quality selected as a principle of Classification is not usu- 
ally an obvious or conspicuous trait. The casual observer 
would generally think tliat it was small and insignificant. 
Thus, the Botanist, disregai'ding the size, shape, and color 
of trunk, branches, and leaves, founds an important classi- 
fication of plants upon the minute and inidimentary cotyle- 
dons, or seed-coverings. All the Monocotyledons are En- 
dogens, and therefore have in common all the numerous 
traits of that gi'cat tiibe or family ; while the Dicotyledons 
are all Exogens. On the other hand, the number and 
relative position of the stamens and pistils, on which Lin- 
naeus founded his artificial system, are not found to be 
invariably joined with any important features in the organ- 
ization of the vegetable kingdom. It should be observed, 
however, that classifications are framed for different uses ; 
and the peculiar nature of the purpose in view may justify 
an arrangement that would be otherwise indefensible. 
Thus, the alphabetical order is the only convenient one for 
a dictionary ; bvit only such classifications of words are 
properly scientific as are found in Logic and Grammar. 

In order to carry on the Classification, and erect a hie- 



324 APPLIED LOGIC. 

rarchy of Concepts of many ascending steps, it is absolutely 
essential that the Infima Species, or class first formed, 
should embrace only those individuals which have, at least, 
several common attributes. There must be, at least, as 
many of these attributes as will furnish a Specific Differ- 
ence for each step in the ascending scale. 

Passing now from the science of coexistent objects to 
that of events which succeed one another in time, we come 
upon a totally different principle of connection. In the 
former case, it was the Concept of substance ; in the pres- 
ent one, it is that of causation. It belongs to Metaphysics 
rather than to Logic to explain the peculiar nature of the 
relation of Cause and Effect. Here it is enough to say, 
that the connection between them is conceived to be abso- 
lute or necessary ; where the Cause exists, the Effect must 
follow, and the presence of the Effect is inconceivable un- 
less the Cause immediately precedes it. But causation^ as 
well as substance^ is incognizable through the perceptions of 
sense. In the outward world, at least, we never can per- 
ceive the nexus, the bond of union which compels the Effect 
to follow. We beheve that it exists, and that the connec- 
tion is a necessary one ; but we are compelled to infer its 
existence from the invariableness of the sequence in time 
between the two events. If heat is applied to wax, the 
wax always melts ; if poison in sufficient quantity is taken 
into the stomach, the man invariably dies. Hence we are 
led to believe that the heat causes the melting, and the 
poison causes the death ; or, in other words, that the sub- 
sequent event is the necessary result of some power or force 
in the antecedent, which, though it cannot be perceived by 
us, inevitably produces this phenomenon. If heat be a true 
Cause, the melting of the wax must follow ; but as far as 
our experience, and, if human testimony may be believed, 
as far as all human experience has gone, the melting always 
does follow ; therefore, the heat is the Cause. On such 



APPLIED LOGIC. 325 

reasoning as this, all our evidence of physical causation — 
i. e. of Causation in the material universe — depends. But 
it is obvious that the reasoning is illogical and the evidence 
is insufficient. Human experience is limited; it extends 
only to a certain number of cases, — no matter to how 
many, as the number is certainly finite. Any number of 
instances of actual measurement would never satisfy the 
geometer that the three angles of a triangle must equal two 
right angles. It is conceivable — nay, the case has actu- 
ally happened — that, after one hundred millions of favor- 
able instances occurring in uninterrupted succession, the 
liundred-million-and-first instance should be an exception, 
or one of an opposite character. Mr. Babbage tells us that 
his Calculating Machine may be so adjusted that, when put 
in regular motion by the descent of a weight, it will pre- 
sent to the eye successively the series of natural numbers, 
1, 2, 3, 4, 5, «&c. ; that, if we should have patience and time 
to watch it long enough, we should find that it would 
present this series in one unbroken chain from 1 up to 
100,000,000, each term exceeding its antecedent by unity. 
Now an induction extending successively to 100,000,000 
terms, without a single inconformable instance being dis- 
covered, would be regarded by most persons as equivalent 
to a demonstration that the law of the series was universal 
or absolute. But in fact, the next number presented, 
after 100,000,001, instead of being 100,000,002 would be 
100,010,002, and the next term would be 100,030,003. 
Human experience, then, as it is limited to a finite number 
of cases, can never establish an absolute law, or prove that 
a certain result is necessary. As the very idea of Efficient 
Causation involves that of the necessary consequence of the 
Effect, it follows that the range of human experience in 
the material universe does not extend to the discovery of 
Causes properly so called. 

In all the Physical Sciences, then, causation should be 



326 APPLIED LOGIC. 

understood to mean only constant conjunction in time. We 
cannot even declare that this conjunction is absolutely 
invariable ; all that can be said is, that it Aas heen invari- 
able so far as human observation has extended, and we 
may firmly believe that no instance will ever be found to 
the contrary. But this is not a necessary belief; its con- 
tradictory neither ^dolates any Law of Thought, nor any of 
the primitive and ineradicable laws of human belief. The 
assumed invariability of what are called " the laws of na- 
ture " rests upon no foundation whatever but uniform ex- 
perience, and is absolutely certain, therefore, only to the 
extent of that experience. That a Law of Nature may here- 
after be violated, or be altogether changed, is not merely 
conceivable; we say as much as that of any Judgment 
which does not contradict one of the Axioms of Pure 
Thought. Such a violation or change must be pronounced 
to be possible., though not probable. Our only reason, for 
instance, for believing that sugar always will be soluble in 
water, and that powdered chalk, under the same circum- 
stances, will always be insoluble, is, that, though a vast 
number of experiments have been tried, we have not, as 
yet., known or heard of one instance to the contrary. 

But in the strict meaning of the word cause., — that is, 
efficient cause, — what is called the Law of Causation is 
absolute ; it is, in the strictest meaning of the term, impos- 
sible tliat any event should take place without a true 
Cause. I do not say that the contradictory of this Law 
would violate any Axiom of Pure Thought ; for as we are 
now concerned, not with the Form, but with the Matter, 
of Thought, these Axioms are inappHcable. But it may 
be said that the Law of Causation is held to be inviolable 
by what I have here called " the primitive and ineradicable 
laws of human belief." It is, for instance, just as impos- 
sible for us to believe that an event should take place with- 
out a Cause, as it is to believe that any particular space 



APPLIED LOGIC. 327 

sliould be annihilated, or that what I am now conscious of 
does not really exist as a mental phenomenon. He who 
can believe that space has hmits or boundaries beyond 
which there is no space, or that he himself does not exist 
as a thinking being, may also believe that a physical event 
can take place without a Cause ; no sane person is capable 
of crediting either of these propositions. 

The distinction here established would seem to authorize 
some change of the phraseology usually employed in Phys- 
ical Science. What has hitherto been denominated, not 
only by physicists, but by people generally, a cause, might 
more properly be called a constant condition, of the phe- 
nomenon. What the physical inquirer is really in search of, 
when he is inquiring after what he calls the cause of any 
event, is a constant antecedent of it, which, being discovered, 
will ever afterwards enable him, should not the sequence 
of antecedent and consequent be altered, (and of this he 
justly entertains no fears whatever,) to predict the recur- 
rence of the phenomenon. To him, the Law of Causa- 
tion, to adopt Mr. J. S. Mill's language, means only this : 
" For every event, there exists some combination of events, 
some given concurrence of circumstances, positive and neg- 
ative, the occiuTence of which will always be followed by 
that phenomenon." Under this view, the so-called Laws 
of Nature might more properly be denominated General 
Facts, as the word " law " generally implies what is abso- 
lute or necessary. But as any sweeping change of scien- 
tific phraseology is hardly to be expected, the language 
heretofore in use must continue to be employed, though 
under protest from those who understand the impropriety 
of its application. There may be Laws of Nature which 
are absolutely invariable ; but it is certain that none such 
have been, or ever can be, discovered. Human science is 
merely able to establish certain General Facts, which are 
indisputably time only to the extent of our experience. 



328 APPLIED LOGIC. 

We shall hereafter examine some of the reasons which 
have caused a higher degree of certainty and generality 
to be attributed to these Facts than they actually deserve. 

It is manifest from what has been said, that Science is 
made up of two sorts of cognitions, — those in which the 
objects are given as contingent phenomena, and those in 
which the objects are given as necessary facts or laws. 
The former are called empirical^ as they are derived from 
experience, and are true only to the extent of that experi- 
ence. Their origin is also said to be a posteriori^ because 
they are subsequent to experience. The latter are said to 
be a priori in origin, for although first manifested on occa- 
sion of experience, they are truly prior to it ; for if they 
had not previously existed, as native to the mind and in- 
wrought into its very constitution, experience itself would 
not have been possible. We have already had examples 
of such, in our notions of substance, cause, space, time, &c. 
These may be expressed, as here, each by a single term 
which is significant of one act of the mind, — an indivisible 
Intuition or Thought; or they may be resolved into one 
or more Judgments, as statements of necessary laws. Thus, 
the cognition of substance may be resolved into this Law, 
that every real attribute or quality presupposes some sub- 
stance in which it inheres. Cause, as already mentioned, 
ftirnishes the universal and absolute Law of Causation, that 
every physical event or change must have a cause. The In- 
tuition of space yields many necessary Judgments, thus: 
Every physical object must exist in space ; Space is inde- 
structible, even in Thought, as a whole, or in any of its parts; 
Space is boundless; &c. The notion of Time also is re- 
solved into several necessary laws, thus : Every event must 
take place at some determinate point in time ; Time necessa- 
rily flows on in one continuous lapse ; Time is boundless 
both before and after, or, as the Schoolmen say, both a 
parte ante and a parte post ; &c. 



APPLIED LOGIC. 329 

These necessary Laws must be regarded as mere ex- 
plications of theii' respective a priori cognitions ; they are 
not inferences from such cognitions, but are involved in 
them, so that it is impossible to have a full and adequate 
conception of the one — that is, to fully understand the 
meaning of the term — without the other. In neither 
form, as one conception nor as a judgment, can they be de- 
rived from experience ; for experience can only tell me of 
what is true in certain cases, — namely, those cases which 
I or other persons have actually witnessed ; while these 
Laws are known to be absolutely tnie for all cases past, 
present, and future. All the maxims of experience are 
reversible in thought ; that is, I can conceive that their 
opposites or contraries should be true ; — I can conceive, 
for instance, that fire should not burn, that water should 
not drown, that stones should fall upward,* instead of down- 
wards, that " when the brains were out, the man should 
7wt die." But these necessary cognitions a priori are not 
reversible in thought ; I cannot conceive that an attribute 
should exist without a substance, or that space should be 
annihilated, or have limits affixed to it, or that a physical 
event should take place without a Cause. Moreover, as 
has been said, these cognitions are prerequisites of experi- 
ence, without which experience itself would not be possible. 
As no body can exist without space, no quality without a 
substance, I could not have my first experience of either, 
— that is, I could not know body to be body, or quality to 
be quality, — unless these cognitions were already present 
to the mind, althovigh then first drawn out and made dis- 
tinct to consciousness. As the capacity of being exploded 
must be conceived to exist in the gunpowder before the 
actual explosion can take place, although this capacity was 
latent up to that moment, so the cognition of space must 
have been in the mind before we could have a conception 
of hody^ and the cognition of time,, before we could have 
that of an events since every event must be in time. 



330 APPLIED LOGIC. 

And yet these cognitions are not, like the Axioms which 
we formerly considered, mere Laws of thought ; for they are 
necessarily apprehended as actual and immutable Laws of 
real things. It is true, that the attribution of these Laws to 
actual phenomena is an act of thought ; so is all cognition, 
whether of external events and things, or of abstract uni- 
versal principles. Berkeley and other Idealists, then, who 
hold that what we call external realities exist only in 
the mind, may consistently maintain that these a priori 
cognitions are merely necessities of thinking thus and so. 
But the Realist, who believes in the objective validity of 
our external perceptions, who holds that things are what 
they seem to be, cannot consistently deny the objective 
reality of those Forms and Laws without which any external 
existence would be impossible, — which are, in fact, neces- 
sary conditions of the reality of such existence. Hence I 
cannot but regard Kant's elaborate attempt to reduce these 
cognitions to mere Laws of Thought as inconsistent with his 
own doctrine. He affirms that we have no knowledge of 
external realities, and are, therefore, incompetent to pro- 
nounce whether they do, or do not, possess certain attri- 
butes ; and yet he declares that " things in themselves " 
have a real existence apart from our thoughts. He admits 
the distinction between noumena and phenomena, between 
things as they are and things as they appear, and asserts 
the reality of the former, though they are wholly incogniza- 
ble to our minds. But if they are absolutely incognizable, 
how does he know that they do not exist under the Laws of 
space, time, and Cause ; and if they are real, how can they 
exist except under those Laws which are the conditions of 
all reality ? To deny the objective validity of these Laws 
is to contradict the primitive testimony of consciousness, 
and to cut away the foundations of all philosophy, whether 
dogmatic, critical, or sceptical, by impeaching the correct- 
ness of those principles and arguments by which the sceptic 



APPLIED LOGIC. 331 

himself attempts to show the reasonableness of his doubts. 
I have no better and no other reason for affirming that two 
straight lines cannot enclose a space, than for pronouncing 
that space itself exists in some other manner than as a 
mere law of the perceptive faculty. The doctrine of the 
Idealists is at least intelligible ; for I can imagine the an- 
nihilation or non-existence of objects in space ; but the 
non-existence of space itself is literally unthinkable. It is 
a mere paradox to assert the reality of the objects, whose 
existence is contingent, and deny that of space, which 
exists by necessity. And the argument is worse than the 
doctrine which it is offered to support ; since the only rea- 
son alleged for believing space and time to be unreal, is the 
impossibility of thinking that they are unreal. 

In conformity with what has been said, it might seem 
that the doctrine of the formation of Science would prop- 
erly fall into two great divisions ; the one relating to the 
acquisition of contingent knowledge by means of expe- 
rience, and the other to the attainment of necessary 
knowledge by the development and application of those 
primitive tiniths which are revealed to us in the veiy con- 
stitution of our minds. And, in a certain sense, this divis- 
ion exists. Geometry and Arithmetic, as the sciences of 
continuous and discrete quantity, are applied most directly, 
and in their purest form, to the conceptions of space and 
time, in which these two modes of quantity are most 
clearly manifested, not being modified or confused by the 
presence of other attributes. The lapse of time cannot be 
conceived or expressed except by the idea of number^ or 
discrete quantity ; and the extent' of space, in like manner, 
is necessarily conceived as continuous qviantity. And in 
both cases, our conception of pure quantity is most distinct, 
because there are so few other attributes of space and time 
with which it might become confused. But these two 
sciences are not restricted to the consideration of pure 



832 APPLIED LOGIC. 

space and time, and do not exhaust our conceptions of 
them. They relate to space and time only so far as 
these are magnitudes^ or things to be measured ; and they 
relate to everything else, so far forth as any other thing is 
susceptible of measurement. Mathematics itself is the 
science of relative magnitude. Thus, Algebra, which is 
the highest form of mathematical generalization, is the 
science of pure magnitude, or quantity in the abstract, and 
thus includes both Geometry and Arithmetic, since its 
principles and formulas are alike and indiscriminately ap- 
plicable both to space and time. Thus the expression for 
the square of the sum of two quantities, (a -\- b^^ = a^ -\- 
2 ah -\- 6^, holds true alike for continuous and discrete 
quantity, for space and time ; since it is equally an expres- 
sion of the truth, that the square erected upon the sum of 
two lines may always be resolved into two smaller squares 
and two rectangles, corresponding to the formula ; and also 
of that which is only another aspect of the same truth, 
viz. that the arithmetical expression for the square of the 
sum of two numbers may be resolved in precisely the same 
manner. 

It does not appear, then, that what are called the de- 
monstrative sciences owe their attribute of logical certainty 
to the peculiar nature of the subjects about which they are 
conversant. It is not because space and time are at once 
necessaiy conceptions of the intellect and immutable laws 
of real things, that the mathematician is able to build up 
his vast fabric of pure truths, which are absolutely certain 
and are independent of any verification by experience. 
The science of pure quantity, which seems to me the only 
proper definition of mathematics, is also the science of real 
things, but so far only as these are affected by quantity 
and thus subject to measurement, and so far only as this 
measurement is executed with that ideal precision and 
accuracy which are presupposed in every mathematical 



APPLIED LOGIC. 333 

investigation. The necessary and a priori cognitions of 
the human mind do not constitute a department of science 
by themselves, but are interwoven with the empirical ele- 
ments of our knowledge. Their office is not constitutive, 
but regulative. They determine the limits of the under- 
standing, prescribe its functions, and regulate its belief. 
Whatever is apprehended under the relations of Quantity, 
is subject to the immutable laws of Quantity. Whatever is 
known as an event or change, is governed by the necessary 
laws of Causality and Time. Attributes or qualities are 
apprehended under the law of Substance, which determines 
the mode of their existence. It is only by abstraction, or 
disjoining in thought what cannot be separated in reality, 
that a separate science can be created of necessary cog- 
nitions a priori, as in that branch of Metaphysics which is 
called Ontology. 

Going back to the physicist's conception of Cause, that 
is, Invariable Antecedence, we observe that the method of 
distinguishing invariable sequences from accidental ones is 
by analysis. Every event has many antecedents and a 
crowd of concomitant circumstances. We seek to ascertain 
Avhicli of these are necessary conditions of the phenomenon 
by analyzing them ; that is, by trying the experiment over 
again, leaving out each time one or more of the attendant 
circumstances ; if the same result still follows, the circum- 
stances thus left out are not the causes which we are in 
seai'ch of, but were only accidental concomitants, that did 
not at all affect the issue. Proceeding in this manner, 
step by step, we come at last to some of the original ante- 
cedents, which being omitted, the event no longer takes 
place. Then, in common parlance, we are said to have 
discovered the cause of the phenomenon ; strictly speak- 
ing, it is only, so far as we know, its invariable antecedent, 
or a condition of its existence, — perhaps only a condition 
of our knowing that it exists. The whole method is ten- 



334 APPLIED LOGIC. 

tative, and is evidently exposed to error, as it is only an 
application of that fallacious mode of reasoning which has 
been exposed as the sophism post Jioc^ ergo propter hoc. 
Hence, the conclusion is not held to be established for the 
purposes of science, until the experiment has been tried, or 
the observation repeated, under every possible variety of 
circumstances. But a large experience, especially if con- 
firmed by some analogy between this phenomenon and 
others that are known to follow similar antecedents, may 
establish the conclusion beyond all reasonable doubt. 

As our knowledge of the phenomena of succession in- 
creases, the Concepts which we form of individual objects 
and classes of objects become larger and more complex. 
Our conception of any corporeal thing must include not 
only those obvious qualities, such as shape, color, specific 
gravity, texture, &c., which it manifests on nearly all 
occasions, but the changes to which these are subject when 
it is brought in contact with other substances under differ- 
ent circumstances, and also those changes in other bodies 
of which its presence may be a constant antecedent. 
" The ideas," says John Locke, " that make up our com- 
plex notions of corporeal substances are of these three 
sorts. First, the ideas of the primary qualities of things, 
which are discovered by our senses, and are in them even 
when we perceive them not ; such are the bulk, figure, 
number, situation, and motions of the parts of bodies, which 
are really in them, whether we take notice of them or no. 
Secondly, the sensible secondary qualities, which, depend- 
ing on these, are nothing but the powers those substances 
have to produce several ideas in us by our senses ; which 
ideas are not in the things themselves, otherwise than as 
anything is in its Cause. Thirdly, the aptness we consider 
in any substance to give or receive such alterations of 
primary qualities as that the substance so altered should 
produce in us different ideas from what it did before ; these 



APPLIED LOGIC. 335 

are called active and passive powers ; all which powers, so 
far as we have any notice or notion of them, terminate 
only in sensible simple ideas. For whatever alteration a 
loadstone has the power to make in the minute particles of 
iron, we should have no notion of any power it had at all 
to operate on iron, did not its sensible motion discover it ; 
and I doubt not but there are a thousand changes, that 
bodies we daily handle have a power to cause in one 
another, which we never suspect, because they never ap- 
pear in sensible effects." 

" Powers therefore justly make a great part of our com- 
plex ideas of substances. He that will examine his com- 
plex idea of gold, will find several of its ideas that make it 
up to be only powers ; as the power of being melted, but 
of not spending itself in the fire, of being dissolved in aqua 
regia, are ideas as necessary to make up our complex idea 
of gold, as its color and weight ; which, if duly considered, 
are also nothing but different powers. For to speak truly, 
yellowness is not actually in gold, but is a power in gold 
to produce that idea in us by our eyes, when placed in a 
due light ; and the heat which we cannot leave out of our 
idea of the sun is no more really in the sun, than the 
white color it introduces into wax. These are both equally 
powers in the sun, operating, by the motion and figure of 
its sensible parts, so on a man, as to make him have the 
idea of heat, and so on wax, as to make it capable to pro- 
duce in a man the idea of white." * 

A fourth class of the elements that form our Concepts of 
individual objects consists of the Relations in which these 
objects stand to other things. These, of course, are num- 
berless, and therefore are a great source of the indistinctness 
and imperfection of this sort of knowledge. Every object 
may be compared with every other object in nature, and 
with every Concept which the mind has previously formed ; 

* Essay on Uunian Understanding, Book II. Chap. 23, §§ 9 and 10. 



336 APPLIED LOGIC. 

and of the countless Relations thus brought to our notice, 
many are essential to an adequate knowledge of the related 
object. Most of Aristotle's Categories are an imperfect 
attempt to classify these Relations, and place them under 
their summa genera. Some of them, such as those of 
Quantity, Place, and Time, are definite and admit of accu- 
rate determination ; as such, they are the objects of the 
Exact Sciences. Others, hke those of Quality, Posture, 
and Modes of Being, Doing, and Suffering, are wholly 
indeterminate, at least in this respect, that their various 
sorts and degrees are shaded into each other imperceptibly, 
or without any natural lines of demarcation. These, of 
course, can be grouped into classes only in some rough 
and arbitrary way, the divisions not being marked out by 
nature. As our knowledge of them is thus vamie and 
incomplete, our conclusions or inferences concerning them 
must be uncertain, and the Sciences under which they fall 
may be said to be occupied with Contingent Matter. 

In Applied Logic, the test of the adequacy of a Concept 
is its more or less complete enumeration of the essential 
qualities of the real thing, or class of things, which it de- 
notes. Any attempt to ascertain and enumerate all of 
these empirically, or by successive observations and experi- 
ments, is hopeless ; a lifetime would not suffice to accumu- 
late more than a small fraction of such knowledge of a 
single object. Thus, its active and passive powers, as 
they are termed, or, more properly, the fixed Relations of 
antecedence and consequence which subsist between the 
changes affecting it and those affecting all other substances, 
could be ascertained only by placing it in juxtaposition with 
every other thing singly, and with every conceivable com- 
bination of other things. Apply heat or water to some one 
substance taken separately, and only two or three series of 
changes would be observed, such as its greater or less fusi- 
bility, solubility, absorption of heat or fluid, capability of 



APPLIED LOGIC. 337 

being oxidized, &c. But apply the same agents to it in 
combination with one or more other substances, and series 
of very cHfFerent phenomena may be manifested. By rea- 
son of the endless number and variety of such possible 
observations and experiments, the results of them in a vast 
majority of cases being individual truths of no special inter- 
est or importance, no one can think of engaging in them by 
detail, or with a view of exhausting the round of possible 
inquiry and trial ; and hence our knowledge must always 
fall infinitely short of the truth of things. The most im- 
portant single facts of this character now known to man 
were accidentally discovered ; they are the fruits, not of 
study and research, but of mere chance. Hence Ave sel- 
dom know the history of such discoveries, or the person 
who made them. Centui'ies after the attractive power of 
magnetic iron had been known, some one, we know not 
who, happened to observe its polarity, or quality of point- 
ing constantly to the north ; and the result was the inven- 
tion of the mariner's compass. The ancients were familiar 
with the obvious qualities of nitre, sulphur, and charcoal ; 
but some obscui'e alchemist, some time in the fourteenth 
century, happened to mix them together in the right pro- 
portions, and the explosion which ensued taught the world 
the secret of gunpowder. The art of printing was hit 
upon by a similar lucky chance. Yet "these three things," 
says Lord Bacon, " to wit. Printing, Gunpowder, and the 
Mariner's Compass, have changed the whole face and state 
of things throughout the world ; the first in literature, the 
second in warfare, the third in navigation ; whence have 
followed innumerable changes ; insomuch that no empire, 
no sect, no star, seems to have exerted greater power and 
influence in human affairs than these mechanical discov- 
eries." 

But as much the greater number of casual observations 
of individual things reveal only unimportant relations and 

15 V 



338 APPLIED LOGIC. 

qualities, there is no encouragement to pursue and record 
them methodically, in the hope of hitting at last upon 
some one of interest and value. Yet Lord Bacon, misled 
by a few brilliant examples, such as those just cited, seems 
to have required, as the first step towards carrying out his 
new system of inductive research, a "Natural and Experi- 
mental History, sufficient and good, as the foundation of 
all." This " History " was to be a complete record of 
individual observations and experiments, omitting nothing 
on account of its seeming triviality and obviousness, to be 
subsequently digested into " Tables and Arrangements of 
Instances, in such method and order that the understand- 
ing may be able to deal with them." * Upon this vast 
store of crude material, towards furnishing which he him- 
self made a respectable beginning in his Historia Naturalis 
et Experimentalis ad condendam PhiloBophiam^ and his Syl- 
va Sylvarum^ or a Natural History, all the subsequent pro- 
cesses of his Inductive Method were to be expended. 
" Smce there is so great a number and army of particu- 
lars," he observes, " and that army so scattered and dis- 
persed as to distract and confound the understanding, little 
is to be hoped for from the skirmishings and shght attacks 
and desultory movements of the intellect, unless all the 
particulars which pertain to the subject of inquiry shall, 
by means of Tables of Discovery, apt, well arranged, and 
as it were animate, be drawn up and marshalled ; and the 
mind be set to work upon the helps duly prepared and 
digested which these Tables supply." f 

Bacon failed to observe that the minds of all men natu- 
rally and inevitably proceed in great part by this method, as 
is evinced by the construction of language. As we have 
seen, all words properly so called are only the General 
Names of the groups and classes into which we marshal 
and digest our individual observations ; — yet with this 

* Novum Organon, Book II. Aph. x. t W- Book I. Aph. cii. 



APPLIED LOGIC. 339 

improvement upon the system that Bacon recommends, 
that the Concepts thus framed inchide only the original 
and essential attributes, the others being left out as of no 
account, and needlessly burdening the memory by their 
vast nvimber. If experiment or casual observation should 
hereafter determine that one of these omitted elements is 
really of interest and importance, it will then henceforward 
constitute an integral part of the Concept. Every one's 
notion of the magnet now includes its attribute oi polarity. 

Derivative attributes, it has been mentioned, are not 
expressly included in the Intension of a Concept, because 
they are implied and vii'tually contained in their primaries. 
Thus, the numberless properties of every geometric figure 
are reduced, in the Concept which bears the Name of that 
figure, to the two or thre« qualities, constituting its Defini- 
tion, from which they may all be derived by necessary infer- 
ence a priori, or without the aid of actual observation and 
experiment. Down to the time of the Baconian reform in 
the processes of physical science, it seems to have been 
imagined that individual substances or bodies, like geo- 
metnc figures, had each its one or two essential properties, 
which being known, all the others could be immediately 
deduced from them by a purely logical process, without 
any aid from experience. This, in fact, was the meaning of 
the word essence, that internal constitution of a body which 
makes it what it is, or from which all its attributes neces- 
sarily flow. Change the essence of the body, then, and you 
thei'eby change all its properties. To the eye of Omni- 
science, doubtless, there is such an essence ; but it must 
ever remain unknown to man's finite capacities, on account 
of the endless number of unknown attributes with which 
it is intermingled. Those qualities alone appear to us 
essential which ai*e known to be constantly associated with 
a few otliers, either because these others can be deduced 
from them by necessary inference, or because they have 



340 APPLIED LOGIC. 

always been found together in a large experience. In the 
latter case, of course, the conclusion is contingent or un- 
certain, being necessarily true only to the extent of our 
previous observation. In the former case, the conclusion 
is absolute, if, by the hypothesis, all other qualities are 
excluded from the Concept except those which are cer- 
tainly known. In geometry, for instance, the Concept or 
definition of any sohd body includes only its shape and 
magnitude, and supposes that these are accurately deter- 
mined; abstraction is made of all its other qualities, be- 
cause these are not susceptible of perfect determination, 
and we know only from experience how far they associated 
with each other. 

If the Matter of Thought, then, includes real existences, 
or such objects and events as are actually presented to us 
in nature, our conclusions respecting them, being derived 
only from experience, must always be subject to doubt. 
As we know them only imperfectly, our inferences respect- 
ing them can never be logically certain. But if the Con- 
cepts are hmited to imaginary objects, consisting only of a 
few perfectly determinate qualities, our conclusions respect- 
ing them will be absolute, though they will be applicable 
only in the realm of pure abstractions. Bacon was right, 
then, in maintaining that the Physical Sciences, so far as 
they extend to the knowledge of real objects, are dependent 
solely upon observation and experiment. " Man, being 
the servant and interpreter of Nature, can do and under- 
stand so much only as he has observed, either in fact or in 
thought, of the course of Nature ; beyond this, he cannot 
understand or do anything." 

We can now see what are the preliminary classifications 
upon the formation of which all Science depends, and can 
point out the principles which regulate this formation. 

1. We form classes of real things or Natural Objects, 
arranging them according to the similarity of their attri- 



APPLIED LOGIC. 341 

butes, and selecting by preference, as the basis of the clas- 
sification, those qualities M'hich are invariably found con- 
joined with the greatest number of other uniform qualities ; 
as the presence of one of these constant elements enables 
us to infer, in anticipation of experience, that it will be 
found in conjunction with those others. TJie science of 
Natural History, in its various departments, consists exclu- 
sively of such classifications, together with such descriptions 
and definitions as are subsidiary to them. 

2. We classify the qualities themselves, according to 
their similarities, irrespective of the real objects in which 
they inhere. Thus, we form classes of colors, sounds, 
shape, and dimension, degrees of consistency, specific grav- 
ity, &c. Sometimes a single set of these arrangements is 
found important enough to be made the basis of a distinct 
science, as in the case of Acoustics and Optics ; more fre- 
quently, several sets of them are grouped together for 
scientific consideration, as is "the case with the chemical 
qualities of substances. 

3. We classify events according to the uniformity of 
their succession in time. These, if regarded as mere se- 
quences of phenomena, may be referred to the subsequent 
head of Relations ; if regarded as the active or passive 
powers of bodies, they may be placed under the preceding 
liead of Qualities. A constant order of succession is often 
erroneously supposed to be a necessary sequence, because 
the mind superadds in such cases its pure conception of the 
necessary relations of Cause and Effect ; and hence sciences 
based upon such classifications are improperly termed 
sciences of causation. Several departments of Physics, 
such as the sciences of Mechanics and Hydrostatics, and 
some divisions of the moral sciences, such as Politics and 
Civil History, are made up chiefly of classifications of this 
sort. 

4. We Classify the relations of things, irrespective of the 



342 APPLIED LOGIC. 

other Qualities and differences of the things related. Thus, 
Geography is, in the main, a classification of the Relations 
of the different portions of the earth's surface to each other ; 
Astronomy takes a similar view of the Relations between 
the different members of the solar and stellar systems. A 
large portion of the sciences of Law and Politics has regard 
to the different Relations which subsist between human 
beings, such as those of husband and wife, parent and 
child, rulers and subjects, countrymen and aliens, &c. 
The mind takes special cognizance only of a very few of 
the countless Relations which comparison and reflection 
bring to hght. We select those only which happen to be 
of special interest to us, through the guidance which they 
afford for our future conduct, the wonder and curiosity 
which they excite, or the bearing which they may have in 
any way upon our welfare. 

It is not meant that each one of the Classes and Sciences 
which we form consists exclusively of one or the other of 
the four species here enumerated. Indeed, the division 
itself is a very imperfect one, for the Dividing Members, 
as we have intimated, do not exclude each other ; a Con- 
cept of Real Things includes a view of their Qualities, their 
active and passive Powers, and their Relations ; and the 
two latter may be comprised under the name of Qualities. 
But these four, sometimes separately and sometimes in 
combination, are the elements which we group together 
into classes, out of which those higher classes, or hierar- 
chies of Concepts, which we call Sciences, are subsequently 
erected. In every case, the classifying principle is simi- 
larity, or uniformity of succession, those Objects and Quali- 
ties being united which resemble each other in certain 
respects, and those events being reduced to the same head 
which uniformly follow one another under similar circum- 
stances. The education of every human being consists in 
the gradual acquisition of a large stock of thesp elementary 



APPLIED LOGIC. 343 

Concepts, which are taught to him in learning the use of 
his mother-tongue, while exercising at the same time his 
powers of observation and reflection. 

The advancement of Science depends on the success of 
the attempts which man is constantly making to enlarge 
and improve the classifications which are the bases of these 
Concepts. By detecting hitherto unobserved similarities 
and conjunctions in time, we extend the generalizations 
and reduce the number of classes, thereby bringing the 
uifinitude of objects and events which nature offers us 
more nearly within the grasp of the human intellect. 
Sometimes the principle itself, or the Ground of Division, 
which determines the classification of a whole set of phe- 
nomena, is altered; as we find a greater number of the 
attributes of these phenomena to be in constant companion- 
slijp with some one or more traits hitherto disregarded as 
of little account, a differently constituted hierarchy of Con- 
cepts, founded upon these traits, is adopted. This may be 
called an improvement in the Method, rather than an 
actual enlai'gement of the domain, of Science. Thus the 
Natural System was substituted for the Linngean classifica- 
tion of plants, and an improvement almost equally exten- 
sive was made by Cuvier in the arrangement of the ani- 
mal kingdom. But most of the questions and problems 
which Science encounters in its progress relate to suc- 
cessive improvements and extensions of the classification 
which, in all its main features, was long since formed, and 
not to the substitution of an entirely different one in its 
place. The fixedness of language, which stereotypes, as it 
were, the names and phraseology appropriated to the old 
division, is a great obstacle to the introduction of a new 
one, which would require a new set of words. The prin- 
cipal object of the reseai'ches of Science is to determine 
whether this or that object, or class of objects, has the 
special characteristics which entitle it to be placed in a 



844 APPLIED LOGIC. 

certain class, and therefore to be called by tlie name of 
tliat class. For instance: — Is the lightning to be placed 
in the class of electrical phenomena? Can the revolution 
of the planets be reduced to the phenomena of falling 
bodies ? Is light the undulatory movement of an ether ? 
Are the processes of digestion and assimilation reducible 
to the ordinary action of chemical affinities ? Ought the 
relation of a motive to a volition to be classed Avith the 
relations of cause and effect, or with those of mere ante- 
cedence and consequence ? 

Such questions relate, for the most part, not to some one 
object or event, but to whole classes of phenomena, and 
therefore presuppose a classification already formed. Some- 
times, indeed, one particular phenomenon of an anomalous 
character may now be observed for the first time ; and 
then the purpose of the inquiry is, to refer it to its proper 
class, and call it by its right name. But such inquiries be- 
long usually to the education of a child, who has not yet 
acquired the amount of knowledge long since possessed by 
his elders, and embodied by them in language through the 
appropriation of names to the different Concepts. But 
Science advances almost exclusively by the resolution of 
problems which concern whole classes of objects, and a 
single phenomenon is observed and experimented upon 
only as a typical specimen of its class, and therefore, as 
leading to conclusions which affect all that are called by 
the same name. Thus, Franklin experimented with his 
kite upon a particular thunder-cloud, but only because this 
one represented to his mind the whole class of meteoro- 
logical phenomena whose characteristics he was investi- 
gating. This, indeed, is the difference between the intel- 
lect of a common man and that of a philosopher. The 
latter flies at once to generalities ; the former wonders at 
the individual case, and seldom goes beyond it. 

" From the moment an isolated fact is discovered," says 



APPLIED LOGIC. 345 

Hamilton, " we endeavor to refer it to other facts which it 
resembles. Until this be accomplished, we do not view it 
as understood. This is the case, for example, with sulphur, 
which, in a certain degree of temperature, melts like other 
bodies ; but at a higher degree of heat, instead of evapo- 
rating, again consolidates." Another example may be 
taken from the General Fact, which some will call a Law 
of Nature, that all bodies give out heat on passing from a 
gaseous to a liquid, or from a liquid to a solid, state ; in 
other words, that contraction of bulk is attended or occa- 
sioned by loss of heat, and expansion of bulk by addition 
or absorption of heat. Yet clay is known to contract from 
the application of heat ; and though water contracts in bulk 
when it is cooling down to as low a temperature as 40°, yet 
as it falls below that point it expands again, and in the 
act of congelation there is a sudden and considerable in- 
crease of bulk. Our natural love of unity, or disposition 
to reduce corresponding phenomena to one class or Law, 
does not allow us to rest in the consideration that such 
cases are anomalous, or isolated exceptions. We seek 
either for a ncAv expression of the Law, which shall cover 
also these apparent exceptions, or for the discovery of 
some attribute of these now isolated cases which shall 
harmonize them with the Law as already expressed. When 
the facts are thus generalized, or brought together under 
one Concept and name, " our discontent is quieted," Ham- 
ilton continues, " and we consider the generality itself as 
tantamount to an explanation. Why does this apple fall 
to the ground ? Because all bodies gravitate towards each 
other. Arrived at this General Fact, we inquire no more, 
although ignorant now, as previously, of the cause of gravi- 
tation ; for gravitation is nothing more than a name for a 
General Fact, the zvhi/ of which we know not. A mystery, 
if recognized as universal, would no longer appear myste- 
rious." 

15* 



346 



APPLIED LOGIC. 



We now see how it is that the successive discoveries, 
and consequent enlarged and improved generahzations, of 
Science are embodied, as fast . as they are made, in lan- 
guage, so that we learn them through the simple mode of 
gradually acquiring the use of our mother tongue. This is 
done to some extent by the actual introduction of new 
words and names, these being necessary to designate the 
new groups and Concepts which the improved classification 
requires. But it is effected still more largely by modifying 
and enlarging the connotation of words already in use. 
For a time, these new elements of phraseology are in cur- 
rent use only among a small circle of scientific inquirers, 
whose labors have made them necessary. But gradually 
they creep out into the ordinary dialect of the market, the 
parlor, and the newspaper, and are naturalized there, and 
taught to children as fast as children learn to speak. How 
much more knowledge is now necessarily acquired in learn- 
ing the use of the English language, than was gained from 
such learning only one or two centuries ago ! 

The same considerations of interest and convenience, of 
immediate relation to the curiosity or the physical wants 
of men, which determine us to classify and name some 
of our individual observations and experiences, to the ex- 
clusion of many others, also guide us in the selection of 
those groups of Concepts which we enlarge, develop, and 
methodize into distinct Sciences. As many objects and 
events do not need to be classified because they are not 
worth remembrance, so the classification of many others 
needs not to be extended beyond the first and most ele- 
mentary stage, because a Science elaborated out of them 
would neither interest us nor minister to our necessities. 
We do not chronicle petty occurrences, we do not study 
out and subsequently generalize the insignificant relations 
of unimportant objects to each other. But as circum- 
stances change and knowledge is enlarged, what formerly 



APPLIED LOGIC. 347 

seemed trivial often assumes a new dignity and interest, 
or is unexpectedly found to be subservient to some great 
purpose. A new Science, or department of Science, is thus 
formed, perhaps to be carried up by subsequent discoveries 
and generalizations higher than any of those formerly cul- 
tivated. How many new departments of study and re- 
search have thus been opened within the last few genera- 
tions ! The Sciences of Geology, Ethnology, Comparative 
Philology, and PoHtical Economy are hardly more than a 
century old. The modems know more than the ancients, 
not so much because they know the same things more per- 
fectly, as because their investigations are extended over a 
larger range of objects. 

Hence it is easy to see why the numerous attempts that 
have been made to classify the Sciences, and thereby to 
reduce them into one complete and orderly system of 
human knowledge, have not been more successful. The 
Sciences have not been fonned on any predetermined and 
systematic plan, with a view of covering the whole ground 
of inquiry ; but they have grown by a natural and irregular 
development, corresponding both to the ever increasing 
wants and stimulated curiosity of those who prosecute 
them, to the different aptitudes of the various classes of 
objects to be digested into system and divided by obvious 
lines of demarcation, and especially to the facility with 
which our conclusions respecting these objects may be 
drawn without the aid of observation and expei'ience. 
Such a survey of all that is possible to be known, com- 
pared with all that is actually known, as Bacon attempted 
to make in his treatise on the " Advancement of the Sci- 
ences," must always disclose, as it did to him, many lacunce^ 
or gaps which it is necessary to fill, before man can be said 
even to have entered upon all the avenues which lead to 
truth. Divisions of the Sciences, like those which have 
been devised by Bacon, Locke, AmpSre, Comte, Wilson, 



348 APPLIED LOGIC. 

and others, must always be imperfect, or, if tliej approxi- 
mate completeness, must always indicate at least as many 
Llanks as there are departments already occupied. Whether 
we try to distribute the various branches of knowledge, as 
Bacon did, according to the different faculties of the mind 
which they respectively call into play ; or, with Locke, 
according to the several ends in view ; or, with Descartes, 
as followed by Comte, according to the order of their de- 
velopment, as determined by their degi'ees of simplicity ; — 
some Sciences will appear redundant, others as defective, 
and many as having an equally good title to be ranked 
under two or three different heads. 

As one of the best specimens of these attempts at 
classification, we may take Dr. Thomson's account of the 
arrangement proposed by Comte, on the basis of Descartes's 
aphorism, that knowledge should advance from the simpler 
to the more complex phenomena. 

" Mathematics, or the science of quantities, is at once the 
most simple in its elements and the most general in its ap- 
plication, entering, more or less, into all the sciences of Na- 
ture, and constituting almost the whole of that which comes 
next it m the order of dependence. Astronomy, or the 
science of the heavenly bodies, is the application of mathe- 
matical truths to the laws of matter and motion ; matter 
and the motions of material bodies being the new concep- 
tions which belong to this science. Physics, being the 
science, or rather group of sciences, which is conversant 
with the general laws of the world, so far as they i^elate to 
beings without life or organization, would come next ; and 
it imports, in addition to the conceptions of Astronomy, 
those of light, of heat, of sound, of electricity, of magnetism, 
and many others. Chemistry would rank next, which is 
the science of the decomposition and combinations of the 
various substances that compose and surround the earth. 
Next in order of complexity would rank Physiology, founded 



APPLIED LOGIC. 349 

on the additional conception of vegetable and animal life. 
To this would succeed Anthropology, or the science of 
man's nature ; and to this, Social Science, which ascertains 
the laws that govern men when combined in cities and na- 
tions. Each of these departments may be divided into 
many branches ; as Physics into Acoustics, Optics, Elec- 
tricity, and the like ; or Social Science into Morals, Poh- 
tics. Political Economy, Law, and the like. 

" On comparing scientific works, differences in the mode 
of teaching the same subject become apparent. In one, 
the pure theoiy of Astronomy is presented ; in another, the 
striking features of its historical progress as a science, with 
speculations on the historical sequence of the phenomena 
themselves ; in a third, the practical applications of which 
the Science admits in respect to the comfort and progress of 
mankind. This threefold mode of treatment runs through 
all the Sciences, and in a table of them might well be ex- 
pressed. The classification would thus embody all that is 
valuable of another system of classes, that according to the 
purpose towards which the Science was directed. 

"A classification which advances on Descartes's principle, 
from the more simple to the more complex subjects, which 
commences from the notions of extension and quantity, 
and proceeds through material things up to living, intelli- 
gent, and moral agents, ought to coincide with the order 
in which the sciences themselves have reached maturity. 
And this it certainly does. Mathematics had made good 
its ground when Astronomy was yet in its infancy ; Physics 
beiran to obtain a sure footino; later than either ; whilst the 
Sciences which relate to Life are still very immature ; and 
some of the main problems of Social Science are yet mat- 
ter of controversy even in our own days." 

It is an obvious imperfection of this scheme, that it takes 
no notice of the numerous branches of that Science, Natu- 
ral Histor}^, which, as it depends solely upon observation, 



350 



APPLIED LOGIC. 



and thus gives us our first knowledge of all the objects of 
study, would seem to constitute the basis of all the other 
Sciences. In explanation of this defect, Comte remarks, 
" we must distinguish between the two classes of Natural 
Science ; — the abstract or general, which have for their 
object the discovery of the Laws which regulate phenomena 
in all conceivable cases; and the concrete, particular, or 
descriptive, which are sometimes called Natural Sciences 
in a restricted sense, whose function it is to apply these 
Laws to the actual history of existing beings. The first 
are fiindamental ; and our business is with them alone, as 
the second are derived, and, however important, not rising 
into the rank of our subjects of contemplation. We shall 
treat of Physiology, bat not of Botany and Zoology, which 
are derived from it. We shall treat of Chemistry, but not 
of Mineralogy, which is secondary to it." But this remark 
is inconsistent with the previous assertion, that this order 
of classification " coincides with the order in which the 
Sciences themselves have reached maturity." In the order 
of time, certainly, Zoology and Botany had been cultivated 
to a considerable extent before men had obtained more 
than the crudest notions of the physiological processes of 
animal and vegetable life ; just as Civil History, the basis 
of another department, had been very fally treated before it 
first suggested the idea of Social Science. In what may 
be called the logical order, or the order of ideas, however, 
it is true that the Sciences which embody principles and 
general results take precedence of those which afford only 
the material of knowledge. 



DEMONSTRATIVE REASONING. 351 



CHAPTER XI. 

DEMONSTRATIVE REASONING AND DEDUCTIVE EVIDENCE. 

WE have already said, that the principal object of tlie 
researches of Science is, to determine whether tliis 
or that object, or class of objects, has the special character- 
istics which entitle it to be placed in a certain class, and 
called by a certain name. 

Most of such questions, if they relate only to one thing, 
or to a very few things, are answered directly, and with- 
out difficulty, by observation or intuition. We answer one 
of them, in fact, whenever we perceive any object and call 
it by its appropriate Common Name. For instance ; — this 
thing which I now hold in my hand I call a pen, a rose, or 
an apple, because I perceive that it has the attributes Avhich 
are the Marks connoted by that name. In like manner, I 
pronounce the animals now before me to be dogs, horses, or 
cows, according as I recognize their distinctive qualities. 

Writers like Dr. Brown, Mr. J. S. Mill, and Mr. Bailey, 
who have laboriously attempted to restrict the range and 
depreciate the utility of the Syllogistic process, have seem- 
ingly failed to notice the fact, that we must reason syllogis- 
tically whenever we use language with any perception of 
its meaning, — that is, when we call anything by its appro- 
priate name. If I had not already spread out before my 
mind the Marks which constitute the Intension of the 
Concept apple, or rose, I could not designate the object 
now presented to me by that appellation. This process of 
reasoning, which we are performing almost every moment 



352 DEMONSTEATIVE REASONING 

of our lives, and therefore so quickly and easily that its 
several steps are taken almost unconsciously, is thus spi'ead 
out into the formal process. 

The Concept or Class-notion apple has, as Marks, a 
neaj'ly spherical shape, a red color, a moderate hardness, 
and a certain smell ; 

This object has all these Marks ; 

Therefore, this object is an apple. 

This is what Hamilton calls Reasoning in Intension, for, 
in each of the Premises, the Predicate is contained in the 
Subject. Moreover, the Reasoning is not only logical, — 
i. e. valid in Form, but it is also Demonstrative, — i. e. abso- 
lutely certain in respect to its Matter. It is Demonstrative, 
because the Major Term, which is here the Subject of the 
Major Premise, is a Concept or Class-notion, which, being 
a mere creation of the mind, cannot have any other Marks 
or qualities than those which we voluntarily attribute to it. 
As we know by Intuition, that the object has all the Marks 
which we included in the Concept, it is certain that it 
should be designated by the name of that Concept, — that 
is, that it should be included under its Extension. 

On the other hand, if the Reasoning is made to concern, 
not a mere Concept in the mind, but a class of real things^ 
which, as we have seen, always have an unknown and un- 
knowable number of qualities and relations, then I cannot 
be sure that the object in question possesses all these quali- 
ties, but can only doubtfully infer that it has all, because I 
know that it possesses some, of the more important of them. 
An element of uncertainty is introduced ; the Reasoning 
ceases to be Demonstrative, and becomes merely Probable 
or contingent. For instance; — if, in the Major Premise 
of the preceding Syllogism, we say, not " the Concept or 
Class -notion apple,'''' but '■'• All apples''^ — i. e. All the 
actual objects which we have been accustomed to call ap- 
ples — " have a nearly splierical shape, a red color, a mod- 



AND DEDUCTIVE EVIDENCE. 353 

erate hardness, and a certain smell " ; then, though " this 
object has all these Marks," I cannot be sure that " it is an 
apple." It may be only a wax counterfeit, and the decep- 
tion would instantly be detected by the taste^ which quality 
Avas not included in the enumeration. The Reasoning is 
still valid in Form, but the Major Premise is false ; it cov- 
ers up the Fallacy fictcB universalitatis. In order to be 
sure that an object is properly ranked under a given class, 
we must be certain that it contains all the original and 
essential qualities of the objects denoted by the class-name ; 
and this certainty, in the case of real things, is unattain- 
able. In our conception, we may arbitrarily restrict tlie 
meaning of the word apple, so as to exclude the quality of 
taste; and in this sense, the wax counterfeit is properly 
called an apple. But in speaking to others, the word 
would be understood to signify all the qualities possessed 
by the real things, viz. this sort of fruit ; and in this mean- 
ing, the wax substitute is not an apple. 

We can now see why the Reasonings of the mathema- 
tician are Demonstrative, while those of the zoologist, the 
botanist, and other naturalists who deal only with real 
things, are merely Probable or contingent. The Form is 
always the same ; Reasoning, as such, must always be 
Syllogistic ; and when the rules of Pure Logic are duly 
observed, the Consequence, or the mere deduction of the 
Conclusion from the Premises, must be absolutely cer- 
tain. The difference, then, concerns the Premises only, 
the truth of Avhich, as we have seen, is not guaranteed by 
the principles of Logic. The universal rule, that the Mid- 
dle Term must always be distributed, requires that tlie 
pre designation all, or none, should appear in at least one 
of the Premises. Now, our knowledge of real things is 
derived solely from experience ; and experience, as has 
been mentioned, must be restricted, from its very nature, 
to a limited number of examples. In respect to real ob- 



354 DEMONSTRATIVE REASONING 

jects and events, it can never extend eitlier to the inclu- 
sion or tlie exclusion of all ; it can never pronounce with 
certainty either upon all., or none. Only Avith reference to 
a certain class arbitrarily formed by the Understanding, — 
to the very things which I am now thinking of, or which 
I have actually observed, and to none others, — to the 
things which are included under this Definition, and to 
these only, — can the finite understanding of man, so far 
as it is enlightened only by experience, safely pronounce 
upon all or none. Without such limitations, naturalists, 
and all others who seek to educe Science from mere expe- 
rience, can never speak of all or none., without falling into 
the Fallacy ^cte universalitatis. 

The mathematician deals only with certain Concepts of 
Quantity, whether continuous or discrete, which are pre- 
cisely limited and determined by the Definitions that he 
employs. The propositions which he establishes do not 
concern circular objects and triangular objects, which are 
real things, but circles and triangles, which are imaginary 
things as conceived by the Understanding, and which are 
restricted by their Definitions to the possession of those 
qualities only which Thought voluntarily attributes to 
them. Hence, the conclusions which the mathematician 
forms respecting them are not liable to be vitiated by the 
intrusion of any unexpected and counteracting elements. 
Any theorem, therefore, which is proved of owe, must hold 
good of all ; any property which cannot belong to one, can 
be possessed by no7ie, of the class thus defined. The same 
measure of certainty which the student of nature obtains 
by Intuition respecting a single real object, the mathe- 
matician acquires respecting a whole class of imaginary 
objects, because the latter has the assurance, which the for- 
.mer can never attain, that the single object, which he is 
contemplating in Thought, is a perfect representative of its 
whole class ; he has this assurance, because the whole class 



AND DLDUCTIVE EVIDENCE. 355 

exists only in Thought, and are therefore all actually before 
him, or present to consciousness. For example ; this hit 
of iron, I find by du-ect observation, melts at a certain 
temperature ; but it may well happen that another piece 
of iron, quite similar to it in external appearance, may be 
fusible only at a much higher temperature, owing to the 
unsuspected presence with it of a little more, or a little less, 
carbon in composition. But if the angles at the basis of 
this triangle are equal to each other, I know that a corre- 
sponding equality must exist in the case of every other 
figure which conforms to the Definition of an isosceles 
triangle ; for that Definition excludes every disturbing ele- 
ment. The conclusion in this latter case, then, is Univer- 
sal, while in the 'former, it can be only Singular or Par- 
ticular. 

Conclusions which are demonstratively certain and abso- 
lutely universal can be obtained only when we are reason- 
ing about abstract conceptions. In the case of natural 
objects and events, which can be known only through ex- 
perience, we approximate universality and certainty in rea- 
soning only by the aid of Induction and Analogy. The 
lack of certainty is a consequence of the lack of univer- 
sality. No doubt affects the few instances which I am 
now actually observing, or which are present to sense or 
consciousness. Of these, I am as certain as of any conclu- 
sions in arithmetic or geometry. The doubt comes in only 
when I attempt to extend the conclusion from some, which 
I have examined, to all others, of which I know nothing, 
except from testimony, Induction, or Analogy. And this 
doubt is inevitable ; no matter how many cases have been 
examined, experience can never extend to all. The fact 
that all matter gravitates, or has weight, is a truth which 
rests upon as large a testimony from experience as has ever 
been collected. Yet the chemist will readily admit that it 
is not only conceivable, but we may almost say probable^ 



356 DEMONSTRATIVE REASONING 

that some of the imponderable agents, as they are called, — 
heat, light, electricity, &c., — may at last be found to be 
material ; and the astronomer has not yet proved entirely 
to his satisfaction, that the law of gravitation is universal 
throughout the stellar system. From the nature of the case, 
he would say, the fact does not admit of absolute proof. 

It appears, then, that the range of Deductive reasoning 
and Demonstrative proof is not confined to pure Mathe- 
matics. Whenever the objects about which we reason are 
pure Concepts, or mere creations of the intellect, strictly 
limited by Definition, and thus guarded against reference 
to things actually existent in Nature, our conclusions re- 
specting them, if obtained in strict uniformity with logical 
rules, are as absolute as the truths of the multiplication- 
table. But Mathematics, it must be admitted, aflford vastly 
the larger number of conclusions of this class ; in no other 
science is Demonstrative reasoning either carried so far, or 
so fruitful in results. This peculiarity seems to be due 
to the nature of those Concepts, quantity, space, and num- 
ber, with which the mathematician deals. Two of these, 
quantity and number, are universal attributes, as they belong 
to all things, both to objects of sense and consciousness ; and 
the third, space or extension, is an attribute of all external 
things. They are suggested to us on a greater variety of 
occasions than any other qualities, and thus ai'e more fre- 
quent objects of contemplation, and more fiilly determined. 
" Propositions concerning numbers," as Mr. Mill observes, 
" have this remarkable peculiarity, that they are proposi- 
tions concerning all things whatever, — all objects, all ex- 
istences of every kind, known to our experience. All 
things possess quantity ; consist of parts which can be num- 
bered ; and, in that character, possess all the properties 
which are called properties of numbers." 

Again, the various modes, properties, and relations of 
quantity, space, and number admit of being more accurately 



AND DEDUCTIVE EVIDENCE. 357 

defined and clearly determined tlian those of any other 
class of ideas ; they are separable from each other by lines 
of demarcation that cannot be overlooked or mistaken. 
Differences of degree, with which we are chiefly concerned 
in the case of all other qualities, are not by any means so 
definite, as they are shaded into each other by impercep- 
tible gradations ; their minute differences are inappreciable 
either by the senses or by the understanding. But the 
difference between two quantities, whether of number or 
extension, may be reduced as low as we please, and still 
remain as distinct to our apprehension as if it were world- 
wide. 

But the chief peculiarity of these three Concepts, which 
causes them to afford so broad and fruitful a field for De- 
monstrative reasoning, is the measureless variety of accu- 
rately determinable relations in which all their modes stand 
to each other. Any one quantity stands in a perfectly con- 
ceivable ratio — whether it can be exactly expressed in 
numbers or not — to every other quantity, and also has a 
countless number of peculiar relations in which it stands to 
many at once. Attempt to enumerate, for instance, the 
pi-operties of the number 9 ; — that it is the square of 3, 
the square-root of 81, the double of 4|-, the half of 18, 
&c., — and we soon abandon the undertaking in despair. 
And when we come to think of the relations of these rela- 
tions, as in the doctrine of proportions, it becomes evident 
that the properties of quantity are too great to be num- 
bered. The field of investigation is infinite. 

These innumerable and perfectly definite relations, which 
subsist between distinct quantities, furnish an inexhaustible 
number of Middle Terms, through which we obtain, by 
Mediate Inference, such Conclusions as are not apparent at 
a glance, or by direct Intuition. When the geometer, for 
mstance, cannot determine directly the distance fi'om one 
pohit to another, he constructs a triangle, the base of which, 



358 DEMONSTRATIVE REASONING 

with its adjacent angles, as accessible, can be easily meas- 
ured ; and he can then deduce the required distance, or 
the height of the triangle, from the known relations which 
exist between it and the quantities which he has thus di- 
rectly determined. In like manner, the value of one or 
more unknown quantities, symbolically represented in an 
algebraic equation, is deduced from some of the given rela- 
tions which subsist between them and the known quan- 
tities, with which they are taken in connection. Indeed, 
the peculiar function of algebraic science is to determine 
general relations between different groups and classes of 
magnitudes, these general ratios, proportions, and analyses 
being subsequently applied by the geometer and the arith- 
metician to the solution of particular problems. The mere 
construction of a geometrical diagram enables us to see the 
use which is made of one or two known relations between 
several quantities, as means of determining indirectly other 
relations between them which cannot be directly meas- 
ured. The diagram is only a means of making clear to 
our apprehension the fact, that the same straight line, or 
length already determined, is at once the base of a triangle, 
the radius of a circle, the side of a square, &c. ; then this 
line may be used as a Middle Term, or means of proving 
syllogistically what the other properties and dimensions, 
hitherto unascertained, of this triangle, circle, and square 
must be. Thus to ascertain a new property of a former 
object of Thought is to advance a step in the classifications 
which the mind is continually forming, enabling us to refer 
this object, perhaps hitherto anomalous, to its proper class. 
The diagram, indeed, is a Singular instance ; but what it 
enables us to discover is a General Truth ; for, as already 
remarked, we know that this one instance is a perfect rep- 
resentative of its whole class, since that class exists only in 
our Thought, and is therefore perfectly known. The little 
triangle which I am contemplating as drawn on paper cor- 



AND DEDUCTIVE EVIDENCE. 359 

responds perfectly, in all particulars that can be essential for 
the Reasoning, to the magnificent o]ie, having as its base 
line the diameter of the earth's orbit, which the astrono- 
mer, when he would deteimine the distance of a fixed star, 
imagines to be erected in the heavens. 

These considerations appear to me to evince very clearly, 
that the peculiar cogency and fruitfulness of mathematical 
reasoning do not arise, as Kant maintains, from the fact 
that it concerns notliing but Space and Time, and that 
Space and Time exist only in our minds. The sole object 
of this sort of reasoning seems to oe quantity in its various 
forms ; and reasoning would be equally Demonstrative, if 
it related to any other single attribute of things considered 
abstractly, or as we conceive it apart from all other proper- 
ties with which it is united in the actual constitution of 
things. The fact that Quantity is a universal attribute, be- 
longing to all objects of Thought whatever, explains the 
broad scope and general applicability of mathematical rea- 
soning ; while its pecuhar fruitfulness, or the vast number 
of tniths which it brings to light, appears to proceed from 
the countless number and definite character of the relations 
which subsist between different quantities. No other attri- 
bute presents itself so universally, or in modes at once so 
numerous and so distinct, capable alike of indefinite aug- 
mentation and duninution. The field is boundless, and we 
advance over any portion of it with the precision and cer- 
tainty in every movement which admit neither error nor 
doubt. 

The views which have now been presented enable us to 
refute the doctrine, originally proposed, as Mr. Stewart 
thinks, by Leibnitz, that the certainty of mathematical 
reasoning depends upon the fact, that all the evidence on 
which it is supported may be resolved, in the last analysis, 
into the perception of identity ; — "the innumerable vari- 
ety of propositions which have been discovered, or which 



360 DEMONSTRATIVE REASONING 

remain to be discovered in the science, being only diversi- 
fied expressions of the simple formula, a = a.''^ It is ti'ue 
that this theory correctly presents the form, not only of 
mathematical reasoning, but of all reasoning whatever ; 
for we have shown that every Affirmative Judgment, in a 
certain sense, or with reference to the denotation of the 
Concepts which it concerns, is an equation of its two 
Terms. The formula, A is B, to which all conceivable 
Affirmative Judgments may be reduced, is resolvable, in 
this sense, as B equals A, into A = A. But the peculiar 
cogency of mathematical evidence cannot be explained by 
the possession of an attribute which does not distinguish it 
from Moral Reasoning. In reference to the connotation 
of its Terms, a Judgment does not express an equation, 
but the inclusion of an object in a class, and the conse- 
quent possession by that object of the peculiar attributes 
of that class. In this sense, the signification is, not that 
the Subject equals the Predicate, but that it possesses one 
or more of the attributes of the Predicate, or possesses the 
Predicate itself as one of its own attributes. The doctrine 
which we are considering owes its plausibility to a con- 
fusion of the significance of these two very different words, 
identity and equivalence. When the geometer proves the 
area of a circle to be equal to that of a triangle having the 
circumference for its base and the radius for its altitude, 
he certainly does not mean that it is identical with such a 
triangle, but only that it is equivalent to it in a single re- 
spect, — viz. in magnitude ; they are not identical, for, in 
shape, they are wholly unlike. Take even a simpler case, 
which seems more nearly resolvable into an expression of 
identity : 4 = 2 -}- 2. Even here, the meaning is not that 
the two members of the equation are identical, but only 
that the Concept or group four is equivalent in one respect 
— viz. the possession of an equal number of units — to 
the two groups two and two. It is plain that one group 



AND DEDUCTIVE EVIDENCE. 361 

cannot be identical with two groups, or that two distinct 
acts of the mind, each conceiving or grasping together two 
units, cannot be literally the same thing as one mental act 
conceiving fou7\ 

The essential distinction between Pure and Applied 
Mathematics consists in this, that, in the former, our 
tlioughts never go beyond the conception of pure quan- 
tity, or magnitude in the abstract, considered in either of 
its two modes, space or number ; while in the latter, the 
additional quahties of weight, attraction, impenetrability, 
elasticity, density, and many others, are brought in, not 
merely as they are conceived in the mind, but as they 
actually exist, or are manifested, in real things. These 
qualities also, so far as they are viewed in the former light, 
that is, abstractly, as mere Concepts strictly limited by 
Definition, may be reasoned about demonstratively ; though 
it is only in respect to their quantity that the reasoning will 
have any wide range, or be fruitful in conclusions, since 
they have not the numerous and distinctly conceived rela- 
tions which subsist between the innumerable degrees of 
Quantity. But if viewed as actual qualities of real things, 
our knowledge of them is derived merely from experience, 
and must therefore be subject to all the limitations and im- 
perfections of knowledo-e so derived. No Judo-ments con- 
cerning them can be absolute or universal ; they are objects 
only of Probable Reasoning. Previous to expei'ience, we 
could not attribute weight to any material substance, much 
less to all such substances; that every particle of matter 
should attract, would seem no more probable than that it 
should repel, every other particle. This is the source of 
Dr. Whe well's en-or ; because tceight, attraction, impene- 
trability, &c. can be conceived abstractly, and therefore 
be strictly limited by Definitions, and so reasoned about 
demonstratively, he maintains that the Physical Laws of 
Motion are necessary truths, and " capable of demonstra- 

16 



362 



DEMONSTRATIVE REASONING 



tion, like the truths of Geometiy." So they are, if viewed 
as mere Concepts, not necessarily having anything cor- 
responding to them in the outward universe. But if re- 
garded as Physical Laws, expressing the actual phenom- 
ena of real things, they are mere educts from experience, 
can be reasoned about only Inductively, and rest solely 
upon Probable evidence. 

Deduction is not a happily chosen word to indicate the 
characteristic feature of reasoning from Universals to Par- 
ticulars, as contradistinguished from Induction^ whereby we 
reason from Particulars to Generals. In the Syllogism 
which expresses the Form of the latter process, the Con- 
clusion is as much a deduction from the Premises, as in 
the former case. We may speak of a Law, or general rule, 
as deduced from several individual facts, with just as much 
propriety as of facts as deduced from the Law. In either 
case, the Conclusion may be said to depend upon the Prem- 
ises in this sense, that the latter authorize us to proceed to 
the former. But it is a mere figure of speech, and not a 
very happy one, to speak of the Conclusion as so involved 
in the Premises, that the one can be drawn out of, or de- 
duced, from the other. The process is rather an explica- 
tion of what was previously in the mind, whereby two acts 
of Thought are brought into harmony with each other. 
The Subsmnption either includes one or more individuals 
in a class, or excludes them from it ; and the Conclusion 
then states explicitly what is virtually or implicitly thought 
in that act of inclusion or exclusion. The process of rea- 
soning is not so much a mode of evolving a new truth, as 
it is of establishing or proving an old one, by showing how 
much was admitted in the concession of the two Premises 
taken together, or what follows from the act of bringing 
them into harmony. The Conclusion is not authorized by 
either of them taken singly. 

Hence it is a still graver mistake, and one which has 



AND DEDUCTIVE EVmENCE. 363 

given rise to much misunderstanding, to speak of the Con^ 
elusion as deduced from one of its antecedents, from the 
Major Premise only. A Sumption or General Rule is a 
necessary part of every Syllogism ; but it does not by any 
means follow, that this Rule alone implicitly contains all 
the particular Conclusions which are ordinarily said to be 
drawn out of it. The Conclusion is drawn in accordance 
with the Rule, and the latter may, in one sense, be said to 
afford a proof of the former, inasmuch as it evinces that 
the Conclusion, if the truth of the Minor Premise cr Sub- 
sumption is granted, cannot be denied without overthrow- 
ing a general principle the truth of which is presupposed, 
as resting upon the evidence either of Intuition, or of a 
Primary Law of Thought, or of previous Demonstration. 
In one sort of Immediate Inference, that of Subalterna- 
tion, the Premise may be rightly viewed as containing the 
Conclusion, as a whole contains one of its parts, and the 
latter may therefore be held to be deduced from the for- 
mer. But the relation between the Subalternans and the 
Subalternate is very different from that which subsists be- 
tween the Sumption and the Conclusion in a case of Mediate 
Inference. In the latter case, the gist of the reasoning 
does not depend upon any Maxim or First Principle, but 
upon the discovery of a Middle Term, with which both 
Terms of the Conclusion are separately compared. This 
Middle Term is the name of a Class, and the new truth 
which is developed by the reasoning consists in the Sub- 
sumption of the Subject of the Conclusion into that Class, 
and the consequent discovery that it possesses all the attri- 
butes or properties which are connoted by its Name. For 
example : — the geometer, wishing to ascertain the size of 
a certain angle, finds that it is one of the angles of an equi- 
lateral triangle ; this is the Subsumption, and when it is 
accomplished, the discovery is really made and the problem 
solved, for the Conclusion that the angle measures 60° im- 



364 DEMONSTRATIVE REASONING 

mediately follows, in accordance with the General Truths 
already demonstrated, that the three angles of an equilat- 
eral triangle are equal to each other, and that their sum is 
180°. But no manipulation, no analysis, of these Truths 
previously demonstrated would enable hitn to evolve from 
them, without the aid of the classification given in the 
Minor Premise, the measure of this particular angle. 
When the Sumption, instead of being, as in this case, a 
Genei^al Theorem previously demonstrated, happens to be 
one of those Maxims which are called Axioms in Geome- 
try, it is still more evident that it is a meagre and barren 
Rule, from which no fruitful and significant Conclusion 
can properly be deduced. 

I accept, then, to its ftill extent, the doctrine originally 
propounded by John Locke, and adopted and defended in 
our own day by Dugald Stewart, that the Axioms of Ge- 
ometry, and the other very general maxims which are 
usually considered as First Principles in our researches, 
" are not the foundations on which any of the Sciences are 
built, nor at all useful in helping men forward to the dis- 
covery of unknown truths." If Reasoning were an organon 
of discovery, a means for the advancement of truth, its char- 
acteristic feature would appear in the Subsumption, which 
places the Subject of inquiry, hitherto anomalous, or of 
uncertain classification, under a Concept, or, what is the 
same thing, in a class, the attributes of which are known ; 
and the proof that it possesses one or more of the attributes 
of that class then appears by citing the General Rule, 
which is the Major Premise. In other words, each of the 
two Premises in a Syllogism has its own appropriate func- 
tion ; the Minor announces a discovery, a new truth, which 
is always a truth of classification, and the Major cites an 
Axiom, or some other general rule, previously well known, 
which proves some consequence of this new truth, or en- 
ables us to acquiesce, with more or less confidence, in the 



AND DEDUCTIVE EVIDENCE. 365 

announcement of this consequence. If the Major is an 
Axiom properly so called, or a truth previously demon- 
strated, — in either case, having absolute universality and 
certainty, — then the Conclusion, if the Subsumption is 
correct, is demonstrated ; but if it is merely a general rule 
obtained by Induction or Analogy, the Conclusion is merely 
probable. 

The correctness of this analysis will appear, I think, 
from an examination of either of the following Syllogisms. 

1. All electricity may be silently drawn off from any charged 

body, by bringing near to it a sharp-pointed rod. 
Lightning is electricity. 
.*. Lightning may be so discharged. 

2. The nervous fluid will not travel along a tied nerve. 
Electricity will travel along a tied nerve. 

.•• Electricity is not the nervous fluid. 

3. All alternate angles made by one straight line cutting two 

parallel lines are equal. 
ABC and B C E are alternate angles. 
.'.ABC and B C E are equal. 

4. Things which are equal to the same thing are equal to each 

other. 
A B and B C are each equal to C D. 
.'. A B and B C are equal. 

5. Happiness is desirable. 
Virtue is happiness. 

.'. Virtue is desirable. 

It is evident that no one of the General Rules which 
form the Major Premises of these Syllogisms can be "at 
all useful in helping men forward to the discovery of un- 
known truths." The real discovery is announced in the 
Minor Premise, and the connection of the two Premises in 
one act of reasoning is the means of p-oving the Conclu- 
sion, and of assuming it into its proper place under the 
General Rule. It does not appear, then, that Reasoning 



866 DEMONSTRATIVE REASONING 

as such, or as an act of Pure Thought, is a means for the 
advancement of knowledge. This doctrine, indeed, follows 
immediately from the principles that have been already 
laid down. Reasoning as such is one of the processes of 
pure Thought which determine the Form, hut not the Mat- 
ter, of our knowledge. The Matter of Thought is ob- 
tained by Intuition, — by observation through the senses or 
through consciousness. The fact or truth thus discovered 
is announced in the Subsumption, not as first made known 
by it, or as deduced from what was previously known, but 
in order to be proved through the Reasoning process ; that 
is, to he hrought into harmony with our previous hnowledge 
as stated in the Major Premise, and that the same conse- 
quences may he attributed to it which are already hiown to 
follow from all the cases included under that general state- 
ment. 

Accordingly, what Hamilton remarks of the whole doc- 
trine of Logic may be applied to the theory of Reasoning, 
which is but one of the departments of this science. We 
cite again, in reference to one of the parts, what has been 
already quoted in reference to the whole. "An extension 
of any science through [pure Reasoning] is absolutely im- 
possible ; for, by conforming to the logical canons, we ac- 
quire no knowledge, — receive nothing new, but are only 
enabled to render what is already obtained more intelligi- 
ble by analysis and arrangement. [Reasoning] is only the 
negative condition of truth. To attempt by mere [Reason- 
ing] to amplify a science, is an absurdity as great as if we 
should attempt, by a knowledge of the grammatical laws of 
a language, to discover what is written in this language, 
without a perusal of the several writings themselves. But 
though [Reasoning] cannot extend, cannot amplify, a sci- 
ence by the discovery of new facts, it is not to be supposed 
that it does not contribute to the progress of science. The 
progress of the sciences consists not merely in the accunui- 



AND DEDUCTIVE EVIDENCE. 367^ 

latlon of new matter, but likewise in the detection of the 
relations subsistinjr among the materials accumulated ; and 
the reflective abstraction by which this is effected " must 
follow the laws of Reasoning. 

We are now prepared to understand and appreciate 
Locke's doctrine, which has been accepted and ably sup- 
ported by Mr. Bailey and Mr. J. S. Mill, that "the imme- 
diate object of all our reasoning and knowledge is nothing 
but particulars." Locke argues that " the perception of 
the agreement or disagreement of our particular ideas is 
the whole and utmost of all our knowledge. Universality 
is but accidental to it, and consists only in this, that the 
particular ideas about which it is are such as more than 
one particular thing can correspond with and be repre- 
sented by. But the perception of the agreement or dis- 
agreement of any two ideas is equally clear and certain, 
whether either, or both, or neither, of those ideas be capa- 
ble of representing more real beings than one, or no." * 
Mr. Mill says : " We much oftener conclude from particu- 
lars to particulars directly, than through the intermediate 
agency of any general proposition. We are constantly 
reasoning from ourselves to other people, or fi'om one per- 
son to another, without giving ourselves the trouble to 
erect our observations into general maxims of human or 
external nature." f 

The only question here concerns the proper use of words. 
The process of comparing one individual object or event 
with another, and thereby ascertaining some relation be- 
tween them, is unquestionably the first step to knowledge, 
and the only means of enlarging our stock of knowledge. 
But the particular fact thus learned is a fact of observation^ 
not of reasoning. Certainly I do not need to reason, nor, 
in the strict and teclmical sense, to think, in order to per- 

* Essay on Human Understanding, Book IV. Chap. 17, § 8. 
t System of Logic, Book 11. Chap. 3, § 3. 



868 DEMONSTKATIVE REASONING 

ceive that John is taller than Wilham. A brute perceives 
this fact as well as I do, and acts upon it, as in distinguish- 
ing his master. Even if we carry the process one step 
further, and form a Judgment, by subsuming the individual 
object of intuition under a class, through perceiving that it 
affects our senses just as some other objects ranked under 
that class have done, still we are engaged only in enlarging 
and generalizing our knowledge, and not in reasoning prop- 
erly so called. But when we take one step more, and pro- 
ceed to attribute certain qualities to that individual thing, 
which are not now directly perceived in it, but are sup- 
posed to exist in it, because we have noticed them in other 
objects of the same class, we are properly said to reason ; 
the act is one of Mediate Inference. But this act does not 
properly enlarge our knowledge, but only explicates it, by 
bringing ou.t explicitly into Thought what was already vir- 
tually contained in it. By putting an object into a class, 
we have already virtually attributed to it all the qualities 
which belong to that class. 

This doctrine is not inconsistent with what has already 
been maintained, that an act of Reasoning is necessary to 
enable us to call anything by its appropriate Common 
Name. Mere observation cannot teach us what is the 
proper appellation of any object which is now for the first 
time perceived ; its name is not stamped upon it, — is not 
one of its qualities directly percejDtible either by sense or 
consciousness. But by the joint action of our faculties of 
perception and comparison, we are made aware that the 
new object resembles a certain class of previously knoAvn 
objects in all the particulars which are connoted by the 
name of that class, and therefore, that the object may be 
properly subsumed into that class, and called by its name. 

The doctrine of Locke and Mill, then, appears true to 
this extent; — that we certainly compare one individual 
thing with another, and only by such comparison can dis- 



AND DEDUCTIVE EVIDENCE. 869 

coverles be made and knowledge advanced. But that sim- 
ple comparison, and the consequent perception of a relation 
of likeness or unlikeness, is not an act of reasoning. We 
do not, in the technical sense of the term, " conclude from 
particulars to particulars." Before this particular discov- 
ery can be made available for the purposes of Science, — 
before it can be brought into union and harmony with our 
previous stock of knowledge, an act of Pure Thought 

— of Mediate Inference, or Reasoning properly so called 

— is necessary. We must become aware that at least one 
of the two Individuals which were compared together is a 
typical specimen or representative of a whole Class, and 
the corresponding Conclusion must be reached, that the 
other Individual possesses some one or more of the essen- 
tial attributes of that Class. To advance to this Conclu- 
sion is, in one sense, an unimportant step ; for it contains 
nothing new, — it does not increase our knowledge. Hav- 
ing learned the individual fact, that " A and B are both 
equal to C," we do not really make any progress, except in 
the way of systematizing our knowledge, when we add the 
very obvious corollary, that "they are equal to each other," 
since this is but one instance under tlie General Rule, that 
" all which are equal to the same thing are equal to each 
other." But in another respect, this step is far from being 
unimportant. Though we have already virtually attributed 
all the qualities of the class to the individual when we have 
included that individual in the class, so that the technical 
Conclusion only draws out explicitly what was already im- 
plicitly thought, a new act of classification is thus com- 
pleted, and the memory is disburdened of particulars by an 
act of arranging and harmonizing our knowledge. First 
to bring out into distinct consciousness the truths which 
are already, so to speak, within our reach, but in a con- 
fused and undeveloped state, and then to place them under 
their appropriate heads or classes in a methodized system 

16* X 



870 DEMONSTRATIVE REASONING 

of knowledge, is the peculiar office of Reasoning. The 
Conclusion, when once drawn, is obvious enough ; other- 
wise it could not be said to be demonstratively proved. 
But far the greater part of our knowledge exists in this 
half latent semi-developed state ; only by an act of Rea- 
soning can it be drawn forth, proved, and made available 
for use in further inquiry. In respect to utility, it matters 
little whether our stores are positively enlarged, or our 
previous acquisitions are developed, systematized, and ren- 
dered more efficient. I believe that no new truth was 
ever discovered by a direct process of pure Reasoning; 
and, on the other hand, that, without the aids and appli- 
ances furnished by such Reasoning, no progress beyond 
the most elementary steps of Science would have been 
practicable. Good observers discover new facts, but good 
reasoners do most to educate and instruct mankind. 

Of course, the fact of observation on which the Reason- 
ing is based, and which it is the office of the Reasoning to 
develop, is not necessarily one perceptible by sense. The 
mere thinker, who, by some lucky chance or by dint of 
patient reflection, hits upon some relation, hitherto unob- 
served, between two abstract ideas, is just as much a dis- 
coverer, as the chemist who first finds that a metal is the 
basis of an alkali; otherwise, no progress could be made 
in pure mathematics or any other abstract science. The 
naked fact, that the square upon the hypothenuse of a 
right-angled triangle is equal to the sum of the squares 
on the two other sides, was observed and known long be- 
fore Pythagoras first succeeded in proving it, by showing, 
through a series of Middle Terms, that it is reallv involved 
in and harmonizes with some elementary principles, the 
whole compass and meaning of which had not before been 
duly developed. The fact Avas first made known by reflec- 
tive observation, — perhaps by sensible experiment ; but it 
did not become a step in the progress of Science till it had 



AND DEDUCTIVE EVIDENCE. 371 

been proved, or subsumed under some broader principles, 
and thus assigned its due place in a system of knowledge, 
by an act of pure Reasoning. 

To those who have fully considered the doctrine which 
was laid down at the commencement, that Logic is not an 
organon for the discovery of truth, and that it is exclu- 
sively concerned with the Form, and not the Matter, of 
Thought, this discussion may seem to have been needlessly 
prolonged. But it has so long been supposed that the 
admission of the inapplicability of the Syllogistic process 
to the discovery of truth was tantamount to a confession 
of the entu'e inutility of the science, that it seemed worth 
while, even at the expense of some repetition, to prove 
that this supposition was wholly groundless, and to show 
precisely what is the utility of the ends to which mere 
Reasoning is subservient. When Mr. Locke says, " I am 
apt to think that he who should employ all the force of his 
reason only in brandishing of Syllogisms will discover very 
little of that mass of knowledge which lies concealed in the 
secret recesses of nature," we have a right to answer, in 
the words of an acute logician, Mr. J. Walker, of Dublin, 
that " he expresses himself with needless caution. Such a 
man will certainly not discover any of it. And if any im- 
agined that the mere brandishing of Syllogisms could in- 
crease their knowledge, as some of the Schoolmen seemed 
to think, they were indeed very absurd." But to those 
Mdio consider how hmited the range of human knowledge 
would be, if it were confined to isolated facts of observation 
resulting from the compai'ison of one individual thing with 
another, having no connection with each other, often seem- 
ingly at variance, not systematized, not summed up into 
general tniths, and hence incapable of communication by 
language, it will be evident that, without the capacity and 
the constant exercise of Reasoning, mankind would have 
advanced but little beyond the condition of the brutes. 



872 DEMONSTRATIVE REASONING 

It may be useful to enumertite the different classes of 
General Rules which are the Major Premises of all Syllo- 
gisms, and, as such, are not so much the First Principles 
whence all our Conclusions are derived, as they are the 
Ultimate Truths in which all Reasoning terminates. 

1. The first of these classes consists of the Primary 
Laws of Pure Thought, and those secondary or derivative 
maxims into which, in different sciences and for different 
purposes, these Primary Laws are explicated. In Logic, 
as we have seen, both the supreme Canons of Mediate In- 
ference, such as the Dictum de omni et nullo, and the spe- 
cial Rules of various sorts of Syllogisms, are all resolvable, 
in the last analysis, into these Laws of Thought. In like 
manner, the Axioms properly so called of Geometry, that 
" if equals are added to equals, the wholes are equal," " if 
equals are subtracted from equals, the remainders are 
equal," &c., are only varied expressions, explications, or 
immediate consequences, of the Laws of Identity and Non- 
contradiction. 

2. The foregoing maxims are merely analytic or explica- 
tive. The next class consists of synthetic or amphative 
Judgments. These are necessary intuitions of pure rea- 
son, or universal truths known a priori., as resulting from 
the constitution of the mind itself. Such are the Judgments, 
that every event must have a cause, that space is infinite, 
that substance underlies all material atti-ibutes, &c. With 
these I am inclined to rank what have been called Axioms 
— more properly. Assumptions — of geometrical science, 
as they are propositions which the geometer must assume 
to be true, though they cannot be demonsti'ated ; for ex- 
ample, — two straight lines cannot enclose a space ; a 
straight line is the shortest distance between two points ; 
two straight lines cut by a tliu'd line at equal angles, if 
produced, will never meet. 

3. We also reason demonstratively from Definitions, that 



AND DEDUCTIVE EVIDENCE. 373 

is, from explications of the Intension of any C oncepts which 
we see fit to frame. Of course, such Judgments are purely 
analytic, and if they contain no unfounded assumption, 
that the sio-nification thus assijxned to the Names of the 
Concepts is that which is usiially affixed to them in the 
common use of language, or that the Marks enumerated 
are all the original and essential qualities of the real things 
which these Names denote, the Conclusions at which we 
arrive must be demonstratively certain. 

4. The laws, or positive precepts, which emanate from 
any sufficient authority, whether human or divine. These 
are not Judgments, but commands, and, as they are to be 
obeyed at all hazards, and on all occasions, the only ques- 

' tion which can arise respecting them concerns their inter- 
pretation. Of this nature are the injunctions of conscience, 
the laws of the land, and the commands of God, as made 
known in his revealed word. Apart fi'om any doubt which 
may arise concerning the signification of the terms in which 
they are expressed, any Conclusion legitimately deduced 
from such commands must be absolutely valid, since uni- 
versality is of the very nature of law. 

5. Universal propositions previously demonstrated. 

6. Truths of generalization, based upon observation and 
Induction or Analogy. These are true only to the extent 
of our experience, which, as we have seen, never extends 
to all or none. Consequently, these propositions rest only 
upon probable evidence ; and though such evidence be suf- 
ficient for moral certainty, they are not available for Dem- 
onstration strictly so called. We may assume them to 
be universally true, and upon such assumptions may rest 
perfectly vahd syllogisms ; but the Conclusion in such 
cases will have no other or higher certainty than belongs 
to the Major Premise. 

It should be observed, however, that, when we thus 
speak of merely probable evidence, the epithet is used only 



374 DEMONSTRATIVE REASONING 

in its technical sense, and it is not meant that we have 
necessarily less confidence in it than in mathematical Dem- 
onstration. " The word probable, when thus used," says 
Dugald Stewart, " does not imply any deficiency in the 
proof, but only marks the peculiar nature of that proof as 
contradistinguished from another species of evidence. It 
is opposed, not to what is certain, but to what admits of 
being; demonstrated after the manner of mathematicians. 
This differs widely from the meaning annexed to the same 
word in popular discourse ; according to which, whatever 
event is said to be probable is understood to be expected 
with some degree of doubt." Perhaps the clearest distinc- 
tion between Demonstrative and Probable evidence consists 
in the fact, that the former does not admit of degrees, as a 
proposition is either demonstrated absolutely, or not at all ; 
while the latter may exist in any degree, from the faintest 
shade of probability up to moral certainty. 

This seems the proper place for the explanation of 
the technical terms, or Second Intentions of Judgments, 
that are used in the construction of Science. Most of 
these, however, are of infrequent occurrence, except in the 
mathematical sciences. All propositions are either Theo- 
retical or Practical ; — the former are purely speculative, 
the truths which they enounce being merely objects of con- 
templation by the mind, as having no reference to action 
or conduct ; the latter have regard to something which is 
to be done or omitted, to some performance or mode of 
procedure. Propositions are also said to be demonstrable, 
if they require or admit of proof; they are indemonstrable, 
if they are self-evident, or intuitively known. 

An indemonstrable judgment, if theoretical, is called an 
Axiom; if practical, it is styled a Postulate. A demon- 
strable judgment, or one which is announced as needing 
proof, if theoretical, is called a Theorem; if practical, it is 
a Problem. A Thesis coincides very nearly with a Theo- 



AND DEDUCTIVE EVIDENCE. 3T^. 

rem ; it is a judgment proposed for discussion and proof. 
A Corollary is a truth announced as an immediate conse- 
quence or collateral result of another judgment that has 
just been proved, and therefore as not needing any sepa- 
rate proof for itself. A Judgment which does not properly 
belong to the science in which it appears, but is borrowed 
from some other, is called a Lemma; one which merely 
illustrates the science, but is not an integral part of it, is a 
Scholion. An EJypoihesis is a judgment not known to be 
true, but accepted for the time as a provisional explanation 
of some phenomena, and as liable to be modified or rejected 
altogether on the production of further evidence. A The- 
ory^ sometimes incorrectly used as a synonyme for Hypothe- 
sis, is a comprehensive and methodical arrangement of 
some large group of phenomena under their supposed 
Causes and Laws, offered as at least a provisional account 
of them and mode of reducing them to system. " Theoria^ 
rum vires,'''' says Bacon, " arcta et quasi se mutuo sustinente 
partium adaptatione, qud quasi in orbem eohcennt, firman- 
tur" 



376 INDUCTION AND ANALOGY. 



CHAPTER XII. 



INDUCTION AND ANALOGY. 



4 



ANY act of Reasoning strictly so called presupposes the 
universality of its Sumption or Major Premise. If I 
am not absolutely certain that all A are B, then, though 
the Subsumption that C is A be undoubtedly true, I can- 
not be sure that C is B. 

Now it has been repeatedly proved, that universal Judg- 
ments cannot be derived from mere experience, which is 
competent to pronounce upon some, or many, but never 
upon all, or none. But as we cannot have any knowledge 
of real things, or actual existences, except by means of 
experience, it follows that such things are not objects of 
Reasoning in the proper sense of the term, — that is, 
of Demonstrative Reasoning, in which the Conclusion is 
accepted with absolute certainty. From the enumeration 
which has just been made, it appears that, with the unim- 
portaijit exceptions of legal precepts and a few truths known 
a priori, all Major Premises must be either mere analytic 
judgments obtained by explicating our own abstract con- 
ceptions, or general rules that are true only to the extent 
our experience. We may assume such rules to be uni- 
irsally true, and the Reasoning will then become perfect 
or Demonstrative in Form; but as the Conclusion can 
never be purged from the shade of uncertainty thrown 
upon it by the imperfect evidence of the universality of 
its Major Premise, such Reasoning is rightly considered as 
merely probable or contingent. We may suppose, also, that 



INDUQTION AND ANALOGY. 377 

the real existences perfectly correspond to the abstract con- 
ceptions that we have formed of them, and, in this way, 
may seem to obtain absolute Conclusions about matters of 
fact. This is commonly said to be reasoning from hypoth- 
eses ; but just so far as such reasoning is Demonstrative, it 
concerns only the Conceptj which cannot be more than an 
imperfect representation of the reality. 

For illustration, I borrow from Mr. Bailey's " Theory 
of Reasoning," page 2, the following examples of Probable 
or contingent Reasonino;. 

1. "I am walking, I will suppose, on the sea-shore, and, perceiv- 

ing a quantity of sea-weed lying on the beach, while the 
water is at the moment a quarter of a mile from it, I con- 
clude that the tide has ebbed, and left the weed where I 
perceive it lying." 

2. " I notice the print of a small foot on the sand, and I feel 

pretty sure that it was made by a child." 

Each of these instances may be resolved into the Form 
of perfect or Demonstrative Reasoning, and it will then be 
seen that the uncertainty which attaches to the Conclusion 
arises solely from the doubt, which experience, however 
often repeated, is incompetent to remove, as to the abso- 
lute universality of the Major Premise. 

1. All sea-weed found within the space usually covered by tlie 

sea at high water must have been left there by the ebbing 
of the tide ; 
This bunch of sea-weed was so found ; therefore, &c. 

2. No small foot-shaped imprint on the sand can have been left 

by anytliing else than the foot of a child ; 
This is a small foot-shaped imprint on the sand ; therefore, &c. 

" In these several cases," says Mr. Bailey, " my mind is 
determined by the sight of present phenomena, conjoined 
with knowledge previously acquired, to believe something 
which I do not actually perceive through the organs of 



378 INDUCTION AND ANALOGY. 

sense ; — something past, something future, or something 
distant ; or, in other words, to believe that some event has 
happened, will happen, or is happening, although beyond 
the sphere of my observation." In short, it is an attempt 
to make the Thinking faculty do the work of the Percej>- 
tive faculty ; to gain a knowledge of an external fact by a 
mere process of Thought, instead of acquiring it by obser- 
vation through the senses. Such an attempt can have but 
imperfect success ; its result is not properly denominated 
hnowledge, but beliefs or opinion. The inference is rightly 
said to rest upon morale or probable^ evidence. 

It is contended by some, that the mind actually rests 
such inferences upon the amount of evidence which has 
really been collected, though conscious that it is incom- 
plete, and does not go through the Form of assumiyig a 
Major Premise which is absolutely universal, and which, 
if we were only sure that it was well founded, would ren- 
der the Conclusion certain. Thus, to recur to one of the 
instances just cited, Mr. Bailey argues that the Premise 
from which the mind actually draws the inference is what 
he terms the Collective Fact, viz. that, in all the eases which 
I have ever observed or heard of, all sea-weed so found has 
been left by the tide, — and not the G-eneral Law, an- 
nounced without this limitation, which affirms as much ab- 
solutely of all sea-weed so found. He maintains that the 
General Law itself, just as much as the particular case in 
question, is an inference from the Collective Fact. To 
rest the inference respecting the individual case upon the 
General Law, does not make the Conclusion a whit more 
probable, than to rest it upon the Collective Fact on which 
this General Law itself is founded. 

Perhaps the question is one which does not merit much 
discussion. Obviously it matters not whether the mind, in 
seeking for competent proof of this particular inference, 
proceeds by throwing what evidence it possesses into the 



INDUCTION AND ANALOGY. 379 

Form of perfect or Demonstrative reasoning, through the 
assumption of a Major Premise which is not free from 
doubt ; or whether it forbears any undue assumption in the 
Premises, and adopts a process of inference which is con- 
fessedly imperfect even in Form. Taking a doubtful asser- 
tion for a Premise, it thus preserves the Form of valid 
reasoning. 

All men are fallible ; 

The author of this book is a man ; 

Therefore the author of this book is fallible. 

Restrict the statement in the Major Premise, so that it 
shall express no more than what is known to be true, and 
the Reasoning thus becomes invalid through an undistrib- 
uted Middle. 

All men, so far as observation has extended, have been fallible ; 
Therefore this author is fallible. 

As a fact, however, I believe the first of these forms is 
much more frequently in use. For proof in any particular 
case, we usually refer to a Law of Nature, the universal- 
ity of which is expressed with as little hesitation as if it 
were a Law of Thought. The usual form of Enthymeme 
employed is the following: — This bit of iron will melt, 
because all iron is fusible ; This water will boil at 212°, 
because water always boils at that temperature ; These 
men must die, for all human beings are mortal. In truth, 
with the exception of those who have made a special study 
of the theory of Reasoning, nobody thinks of restricting 
the universality of such statements by the qualifying clause, 
" so far as has been observed," or " according to all known 
experience." And it is not mere carelessness in the use 
of language, or the proneness to exaggeration which has 
already been pointed out for censure, that causes such 
statements to be made without their proper limit? tions. 
Very few are conscious, even after reflection, that there 



880 INDUCTION AND ANALOGY. 

is any exaggeration in the case ; and there is none, except 
what is implied by adopting the Form, without the sub- 
stance, of Demonstrative Reasoning. 

Induction and Analogy are the two processes of thought 
by which we endeavor to make our Judgments about whole 
classes of real objects, or actual existences, approximate the 
absolute certainty and universality of our Judgments about 
abstract conceptions. Hence they are, what Pure Reason- 
ing is not, organa for the discovery of truth and the actual 
advancement of knowledge. But just so far as they are 
means to these ends, they lose the character of Pure or 
Demonstrative Reasoning; the Syllogisms to which they 
are reducible are faulty either in Matter, as having a 
Major Premise the universality of which is merely proba- 
ble, or in Form, as containing an undistributed Middle. 
The question whether they are entitled to be called Rea- 
soning is hardly worth discussing here, as it concerns only 
the use of words. Logical or Demonstrative Reasoning 
they are not ; but they may be denominated Probable 
Reasoning, or Philosophical Presumptions. 

It should be mentioned, however, that what may be 
termed Logical Induction, the plena enumeratio of the 
logicians, which deduces a General Rule from what is 
known to be true of every individual in the class, belongs 
to Pure Reasoning strictly so called. Conclusions drawn 
from such Premises as the following, are Demonstrative or 
absolutely certain ; but these only generalize our knowl- 
edge, or alter its expression ; they do not enlarge it. 

Mercury, Venus, the Earth, &c. are all the Planets. 
Peter, James, John, Matthew, &c. are all the Apostles. 

This mode of Reasoning has already been analyzed ; but 
it is not what is understood by Induction in the processes 
of Science. Logical Induction concludes from each one to 
all; Induction projierly so called concerns the Matter of 
Thought, and concludes from some to all. 



INDUCTION AND ANALOGY. 381 

The difference between Induction and Analogy has been 
clearly stated and illustrated by Kant. In order to enlarge 
our knowledge beyond the bounds of experience, we must 
either conclude from many things to all others of the same 
Species, which is Induction ; or we must conclude from 
the known agreement of two things in several qualities, 
that they agree also in some other quality which is not 
directly known. In our progress from the Particular to 
the General, Induction proceeds upon the principle, that 
what certainly belongs to many Individuals of the same kind, 
also probably belongs to all the other Individuals of that kind; 
the principle of Analogy is, that, if two things agree in many 
respects, they probably agree also in some other respect. Be- 
cause some one quahty exists in many things, therefore it 
exists in all of the same kind ; this is Induction. Because 
many qualities in this are the same as in that, therefore one 
other quality in this resembles that ; this is Analogy. In 
other words. Induction concludes from one in many to the 
others, by way of Extension ; Analogy, from many in one 
to the others, by way of Intension. 

The following are instances of Induction : — 

1. In many cases in which water has been analyzed, it 
has been found to consist solely of oxygen and hydrogen ; 
therefore, all water is made up from these two elements. 

2. Very many animals have been examined, and these, 
without a single exception, have been found to possess a 
nervous system ; therefore, all animals have a nervous 
system. 

3. Most bodies expand in bulk, if heated ; therefore, 
heat always produces expansion, if it be not counteracted 
by some other cause. 

The following are instances of Analogy : — 
1. The planets Venus and JNIars resemble the earth in 
many respects, as in size, density, time of rotation on the 
axis, distance from the sun, receiving light and heat from 



382 INDUCTION AND ANALOGY. 

it, &c. ; therefore, they probably I'esemble it m one other 
respect, in being inhabited by hving beings. 

2. Fossil skeletons that are found in the rocks bear a 
close resemblance in very many respects to the skeletons 
which, as we know, once belonged to recently living ani- 
mals ; therefore, they resemble them in one other respect, 
in that these fossils are the remains of animals which were 
foraierly living upon the earth. 

3. In many respects, as in complexity of parts, nice ad- 
justment and mutual dependence of these parts one upon 
another, delicacy of finish, symmetry, and adaptation to 
many useful ends, the human hand resembles some inge- 
nious machines, which we know to have been contrived and 
fashioned by the exercise of mind ; therefore the hand was 
so contrived and fashioned. 

4. The argument of Origen and Bishop Butler is, that 
if the Scriptures and the constitution of Nature are alike in 
this respect, that they proceeded from the same Author, 
we may well expect to find the same difficulties in the for- 
mer as are found in the latter. 

It is plain that what is hei'e called Analogy is the same 
mental process which is described and analyzed by Aris- 
totle as " reasoning from Example." He gives the follow- 
ing as an instance of this sort of argument. If we would 
prove that it is not expedient for the Athenians to make 
war upon the Thebans, who are their neighbors, we may 
reason fi-om the analogous case, that the war against the 
Phoceans, who were their neighbors, was fatal to the The- 
bans. He says that Example is not founded, like Syllo- 
gism, upon the relation of the whole to its parts, nor, like 
Induction, upon the relation of the parts to the whole, but 
upon the relation of one part to another, because the one 
is more perfectly known than that other. The Aristotelic 
Induction proceeds from all the individual cases, while Ex- 
ample is founded only upon some of them, perhaps, as 
above, upon a single instance. 



INDUCTION AND ANALOGY. 383 

Comparatively little need be said of Analogy, as the Con- 
clusions to which it leads are evidently not Demonstrative, 
but merely Probable. Strictly speaking, there is no proof 
whatever, because two things resemble each other, how- 
ever nearly, or in however many respects, that the resem- 
blance extends to a single point other than what has been 
actually observed. The existence of one quality, it is true, 
may be necessarily implied in that of another, either by the 
Laws of Thought, or by the a priori laws of the human 
mind ; as one geometrical property of a body may be de- 
duced from another, or as its divisibility may be inferred 
from its extension. This is Demonstrative Reasoning, but it 
is merely explicating our knowledge, and not directly add- 
ing to it ; and certainly it is not reasoning from Analogy, 
which proceeds from similarity in some respects to similar- 
ity in one other, or in many others. Analogical conclu- 
sions may have any degree of probabihty, varying fi'om a 
merely permissible hypothesis up to what may fairly be 
called moral certainty. Because this kind of inference is 
often greatly abused, for some degree of resemblance may 
often be detected between two things apparently most dis- 
similar, — skill in such detection, when the inference is 
ludicrously improbable, constituting wit^ — I am inclined 
to think that the force of which it is susceptible is generally 
underrated. Slight Analogies are worth nothing, except 
to show that the coexistence of two or more qualities is 
barely possible^ no belief whatever being justly created that 
it is probable. On the other hand, the Analogy may be 
so perfect that the Conclusion founded upon it may be ac- 
cepted with as full faith as if it rested upon an extensive 
and cautious Induction, with which, indeed, it is frequently 
confounded. 

To recur to the instances just cited. , The supposition 
that the other planets are inhabited rests upon an Analogy 
which is so faint and imperfect, that it does not afford suffi- 



384 INDUCTION AND ANALOGY. 

cient ground for making up any opinion on the subject, 
either for or against the hypothesis. The resemblance is 
but shght, even in the few particulars that are cited ; and 
we have no evidence that there is any similarity whatever 
in a vast number of other respects, many of which are 
essential to the existence of life under any of the forms 
with which we are acquainted. On the other hand, the 
Analogy between the skeletons that exist only in a fossil 
state, and those of animals now living, is so broad and per- 
fect, that a man's sanity or sincerity would be questioned 
who should affect to doubt that the former also once walked 
the earth or swam in the seas. These fossils do not differ 
more from the extant types than many of the latter do 
from each other, while in the numberless points of Analogy 
the resemblance is perfect. And the conclusion in the 
third case, founded upon the Analogy between the human 
hand and a contrivance of man's device, is still more indis- 
putable. If, without the aid of mind, without foresight or 
design, the mere fortuitous concourse of atoms, in the lapse 
of a past eternity, could have formed a living tree, fish, or 
elephant, then, we say, that same rudderless and purpose- 
less crowd of primeval atoms, in the lapse of a past eter- 
nity, could have formed, what is much easier^ a. fossil tree, 
fish, or elephant. We are here pointing out the analogous 
character of two arguments, each founded upon Analogy, 
but pointing to different Conclusions ; and we find the re- 
semblance between them so perfect, that it is impossible to 
maintain the validity of the Conclusion in the former case, 
and deny it in the latter. 

The definition which is ordinarily given of Analogy, that 
it means proportion, or a similarity of relations, does not 
differ from the one here propounded. Thus, it is said, 
when we affirm the relation of the fins of a fish to the 
water to be the same [similar] to that of the wings of a 
bird to the air, that we are judging from Analogy. So we 



INDUCTION AND ANALOGY. 385 

are ; we are pointing out what is perhaps an unexpected 
resemblance amid apparent diversity. However unhke 
fins are to wings, we still pronounce that they agree in tliis, 
the adaptation of the former to the animal's motion through 
the water being very similar to the fitness of the latter to 
effect motion through the ah'. From this equality of fit- 
ness for corresponding purposes, we reason analogically that, 
if one was contrived by intelligence, the other was also. 

Induction, says Mr. Mill, " may be summarily defined as 
Generalization from Experience. It consists in inferring 
from some individual instances in which a phenomenon is 
observed to occur, that it occurs in all instances of a cer- 
tain class ; namely, in all which resemble the former in 
what are regarded as the matenal circumstances." This 
last qualification is an important one, and has not received 
sufficient notice from those who have speculated upon the 
theory of Induction. The process would be invalid and 
nugatory, if we did not presuppose the correctness of the pre- 
ceding Classifications that have been formed of the objects of 
Science. A conclusion from some to all would not hold, 
would not have even the slightest shade of probability, if it 
were applied to a Class formed of the objects now contained 
in this room, or of those embraced within my present field 
of vision, or of things having no common attribute except 
that they are of the same color, or the same size. But 
such a conclusion becomes extremely probable, even mor- 
ally certain, when applied to a Class, like that of metals 
or stars, having many common characteristics which are 
definite and peculiar. Thus, having ascertained of only 
two metals, iron and copper, that they are conductors of 
electricity, it would be a tolerably safe Induction, that 
all metals are such conductors. Having found that one 
thunder-cloud was electrical, Franklin at once safely leaped 
to the conclusion, that all such clouds had that property. 
We have already seen that the Classifications formed of the 

17 T 



386 INDUCTION AND ANALOGY. 

innumerable objects of thought cannot be arbitrary, but 
must be framed to embrace as many common or similar 
elements as possible. The numberless properties of a 
geometric figure can be deduced by necessary inference 
from the one or two leading properties of it which are 
selected to form its Definition. And the hope always is, 
in forming a Classification of real objects or events in Na- 
ture, to hit upon some attribute as the basis of the arrange- 
ment with which all the other qualities of it are connected 
by some necessary, though to us invisible, tie. 

This appears to afford the solution of a problem which 
has puzzled many inquirers ; — how it is, that we often 
safely frame an Induction from a single instance, while, in 
other cases, the conclusion is precarious, though supported 
by a multitude of affirmative examples. Thus, the chem- 
ist, having discovered a new metal, ascertains by a single 
experiment its specific gravity, degree of hardness, tough- 
ness, &c., and then safely concludes that every other speci- 
men of the metal, which may afterwards be obtained, will 
be found to possess these qualities in the same degree. On 
the other hand, a multitude of instances of recovery from a 
specific disease after the administration of a particular drug 
are insufficient to establish the universal efficacy of the med- 
icine in what appear to be similar cases. In Meteorology, 
also, and in the several branches of Natural History, though 
the Induction may be very extensive, and conducted with 
all possible caution, the general conclusions have only that 
low degree of probability which is indicated by calling 
them empirical laws. The reason of this difference evi- 
dently is, that the Classifications in the science of Chemistry 
approach veiy nearly to perfection, the qualities determina- 
ble by chemical analysis being definite, strongly marked, 
and constant in tlieir forms of combination with each other ; 
while Medicine, Meteorology, and Natural History are, 
and probably must ever remain, sciences very imperfect in 



INDUCTION AND ANALOGY. 387 

Classification, as the objects with wliich they are concerned 
have an indefinite multitude of ill-determined attributes, 
shaded into each other by imperceptible degrees, and com- 
bined in the most irregular manner. The lines, and even 
the principles, of division of the objects of these sciences are 
merely provisional, and ai'e frequently changed, so as to 
adapt them to the progress of observation, or in the hope 
of hitting upon some qualities which may be found in more 
constant I'elations with the other leading properties than 
those which have hitherto formed the basis of the Classifica- 
tion. Of course, the Induction becomes extremely preca- 
rious, when we are not sure that the instances over which 
it extends agree with each other in all material circum- 
stances. 

It is evident, moreover, that the smaller the Class is, or 
the nearer that it comes to an Infima Species, the stronger 
is our assurance that, in reference to this Class, the conclu- 
sion from some to all will hold good. The Induction is 
safer, for instance, from some to all lumps of u-on, than 
from some to all metals ; and it is still more certain in ref- 
erence to all specimens of one kind of iron, wrought or 
malleable, than with respect to all sorts of that metal. As 
the Extension and Intension of the Class-name are in in- 
verse ratio to each other, that is, as the number of attri- 
butes connoted is greater in proportion as the number of 
objects denoted is less, the similarity of the members of the 
Class to each other is increased as the number of those 
members is diminished ; and the greater the similarity, the 
safer the Induction, because it is then more probable that 
the resemblance extends to the material or essential cir- 
cumstances. As the Intension is greater, the Induction is 
founded upon a larger number of qualities, that is, upon a 
more perfect resemblance ; and as the Extension is less, 
the Induction extends to fewer objects, and is therefore 
more likely to be well founded. The gap between sorne 



888 INDUCTION AND ANALOGY. 

and all is not so great, when even all denotes only a few. 
We cannot safely reason, from the process of treatment 
which has been effectual in one case of fever, to the effi- 
ciency of the same treatment in any other instance, merely 
because the symptoms of no one fever-stricken patient have 
anything more than a general resemblance to those of an- 
other; and the internal peculiarities of the malady, of 
which the outward symptoms are only the faint and easily 
mistakable indications, are still more unlike. 

Thus much, however, is certain, that if the Classification 
is correct, if the cases brought together are really parallel 
in all the essential circumstances, — and we must presup- 
pose as much as this before we can reason from Induction 
at all, - — then we firmly believe, and assume it even as an 
axiomatic truth, that " the course of nature is uniform," 
that " natural events are governed by constant general 
laws," that " what has been will be," and that " what has 
been even in one instance has been in all other instances." 
These are only different modes of expressing one and the 
same Universal Truth, — one invincible conviction of the 
human mind. This Truth is the ultimate Major Premise, 
upon which all reasoning from Induction depends, or which 
is taken for granted in all such reasoning. The simplest 
and most indisputable case of such reasoning depends upon 
this Maxim, just as much as the latest and broadest general 
conclusion that has been propounded in physical science, 
though this conclusion may be so questionable that it is 
propounded only as an hypothesis. I gould not be sure, for 
instance, that the identical piece of coin now in my hand 
still possesses the same weight, malleability, hardness, pu- 
rity, &c., which I ascertained from actual observation that 
it had only five minutes ago, if it were not for this irresisti- 
ble belief in the uniformity of nature's laws. Whatever 
doubts may perplex or weaken the inference from some to 
all, these doubts do not concern the Primary Truth upon 



INDUCTION AND ANALOGY. 389 

which all such inferences are based, but relate solely to the 
correctness of the Classification over which the inference 
extends. Is it certain that we have classified rightly ? 
that the cases brought together are really parallel in all 
essential respects ? J£ so, one instance is just as good to 
base an Induction upon as ten thousand ; for we have an 
irresistible conviction that, as the law thus operates in one 
case, it must so operate in all. What is the ground of our 
assumption of this General Truth ? How came we to be 
convmced thus absolutely that nature's course is uniform ? 
He who can answer this question has solved the great 
problem in the philosophy of Induction. 

Dr. Reid, Mr. Stewart, and most of the other Scotch 
philosophers, attempt to resolve our assumption of this 
Maxim into an ultimate fact, into an original and instinc- 
tive law of the human mind. Experience is constantly 
tending to confirm it, but they hold that we believe in it 
previously to all experience. They do not identify it with 
the principle of Causation, — with the law that every event 
must have a Cause, — but maintain that it is a distinct and 
independent Axiom. Dr. Brown even goes so far as to at- 
tempt to resolve the law of Causality itself into this Axiom. 
He asserts that we are obliged to refer every event, every 
beginning to be, to some Cause, because we have an instinc- 
tive anticipation of the uniformity of nature's laws. My 
own opinion, as will be seen hereafter, is exactly the re- 
verse of Brown's theory. It seems to me that our irre- 
sistible conviction of the truth of this Maxim, that nature's 
course is uniform, is resolvable into our necessary belief 
of the law of Causality ; that the latter is the primitive 
judgment a priori, and the former is secondary and de- 
rivative ; that a process of Thought, an act of Reasoning, 
if not an appeal to experience, always precedes, and is 
used to confirm or prove, our assertion that nature's course 
is uniform, while we affirm at once, antecedently to all ex- 



390 INDUCTION AND ANALOGY. 

perience, and without any attempt at proof, that every 
event must have a Cause. 

But however this may be, the doctrine in M'hich Brown 
agrees with Raid and Stewart, that we have an instinctive 
and a priori conviction that nature's laws are imchange- 
able, appears plainly indefensible. JEntia non sunt mul- 
iiplicanda prcBter necessitatem ; it is a cardinal maxim in 
philosophy, that no principle can be admitted as an ulti- 
mate fact until it is clearly shown that it cannot be ex- 
plained as derivative. Indirectly, therefore, this doctrine 
is refuted by the proof, which will subsequently be at- 
tempted, that this principle is resolvable into the law of 
Causality. But still further : — any conviction, which is a 
priori in its origin and character, must be universal, neces- 
sary, and immediate. Now without going so far as Comte 
and Mill, who maintain, with respect to this principle, that 
" far from being the first Induction we make, it is one of 
the last," that "it was only acquired gradually, and ex- 
tended itself, as observation advanced, from one order of 
phenomena to another," and that "there are cases, in 
which we reckon with the most unfailing confidence upoA 
uniformity, and other cases in which we do not count upon 
it at all"; — without adopting these assertions, I say, it 
may safely be pronounced, that we do not accept this prin- 
ciple at first, or in all cases, unless it is justified by some 
reflection or experience ; that is, until we have satisfied 
ourselves that it is a necessary consequence of some intui- 
tive and imperative belief, or have verified it by subsequent 
observations. Through the law of the Association of Ideas, 
it is true, the recurrence of any phenomenon suggests all 
the circumstances by which it was originally accompanied ; 
it may even incline us to believe that these circumstances, 
also, will recur in the same order as before. Even the dog 
cowers at the sight of the whip which has once or twice 
been used to punish him. But this is very far from an 



INDUCTION AND ANALOGY. 391 

immediate and necessarj' conviction that any of these for- 
mer concomitants rmist so recur. We stop to analyze the 
case and make distinctions ; we separate the conjunctions 
that are believed to be invariable from those that are 
merely casual, and accept the former only because we 
recognize one of the events either as a Cause, or what is 
believed to be the regular concomitant of a Cause, of the 
other. 

" Every person's consciousness," says Mr. Mill, "assures 
him that he does not always expect uniformity in the course 
of events ; he does not always believe that the unknown 
will be similar to the known, that the future will resemble 
the past. Nobody believes that the succession of rain and 
fine weather will be the same in every future year as in 
the present. Nobody expects to have the same dreams 
repeated everj^ night. On the contrary, everybody men- 
tions it as something extraordinary, if the course of nature 
is constant, and resembles itself, in these particulars. To 
look for constancy where constancy is not to be expected, 
as, for instance, that a day which has once brought good 
fortune will always be a fortunate day, is justly accounted 
superstition. The course of nature, in truth, is not only 
uniform, it is also infinitely capricious. Some phenomena 
are always seen to recur in the very same combinations in 
which we met with them at first ; others seem altogether 
capricious." 

On the other hand, the doctrine of Comte and Mill, that 
our conviction of the uniformity of nature's laAvs, which is 
the ground or principle upon which all Induction rests, is 
itself obtained by Induction, appears to be an evident beg- 
ging of the question. How can any mental operation be 
used as a means of discovering and verifying a principle 
which must be taken for granted before that operation it- 
self can be performed ? To obtain a number of Conclusions 
by adopting a certain Maxim as a Major Premise, and then 



392 INDUCTION AND ANALOGY. 

to use those very Conclusions as a means of proving that 
Maxim, is evidently reasoning in a circle. Mr. Mill is per- 
fectly aware of this objection to his doctrine, and frankly 
states it in the strongest terms. " Can we prove a prop- 
osition," lie asks, " by an argument which takes it for 
granted ? And if not so proved, on what evidence does it 
rest?" 

But though aware of the objection, it does not appear 
that Mr. Mill has been successful in his endeavors to ob- 
viate it. He rather augments the difficulty, by admitting 
that the Maxim " was not, of course, derived from rigid 
Induction, but from the loose and uncertain mode of Induc- 
tion per enumerationem simplicem.^' Then the Premise 
rests upon less satisfactory evidence than the Conclusion, 
and yet the latter is based exclusively upon the former. 
Is not this a contradiction ? How can the superstructui'e 
be more stable than the very foundation on which it rests ? 

Induction by simple enumeration " consists in ascribing 
the character of general truths to all propositions which are 
true in every instance that we happen to know of." Thus, 
we say that '•^ All ruminating animals divide the hoof," 
merely because no instance to the contraiy has, as yety 
been discovered. But " to Europeans, not many years 
ago, the proposition, 'All swans are white,' appeared an 
equally unequivocal instance of unifonnity in the course 
of nature. Further experience has proved that they were 
mistaken." Then the presumption in favor of what is still 
the accepted rule, in the present state of our knowledge, 
that all ruminating animals divide the hoof, would not be 
held to outweigh the testimony of one unimpeachable wit- 
ness, who should declare that, in some hitherto imperfectly 
explored region, he had discovered a solid-hoofed ruminat- 
ing animal. How can the evidence of these merely pro- 
visional truths, which are liable to be overturned at any 
moment, be the same with that which supports the validity 



INDUCTION AND ANALOGY. 393 

of the Maxim upon which the most rigorous Inductions de- 
pend ? 

Mr. Mill answers, that even this precarious Induction, 
that something is universally true because we have never 
known any instance to the contrary, may become a valid 
gi'ound of belief when it is preceded by the assurance, that, 
" if there were in nature any instances to the contrary, we 
should have known of them." An empirical law, he argues, 
" of which the trath is exemplified at every moment of 
time, and in every variety of place or circumstance, has an 
evidence which surpasses that of the most rigid Induction, 
even if the foundation of scientific Induction were not itself 
laid, as we have seen that it is, in a generalization of this 
very description." As to the admissions made in the pas- 
sage which has just been quoted from Mr. Mill, that we do 
" not always expect uniformity in the course of events," 
and that " the course of nature, in truth, is not only uni- 
form, it is also infinitely capricious," it is claimed that the 
progress of Inductive Science has already explained away 
these apparent exceptions. Tliis progress has been so 
great, it is argued, that we now know directly that the 
Maxim holds good of far the greater number of phenom- 
ena, " the utmost that can be said being that of some we 
cannot positively, from direct evidence, affirm its truth ; 
while phenomenon after phenomenon, as they become bet- 
ter known to us, is constantly passing from the latter class 
into the former ; and in all cases in which that transition 
has not yet taken place, the absence of direct proof is ac- 
counted for by the rarity or the obscurity of the phenomena, 
or our deficient means of observing them, or the logical dif- 
ficulties arising from the complication of the circumstances 
in which they occur." 

But even when the doctrine is thus limited and ex- 
plained, it does not appear to be relieved from the two fiin- 
damental objections which have been urged against it, first, 
17* 



894 INDUCTION AND ANALOGY. 

that it founds the principle of Induction upon Induction 
itself, which is reasoning in a circle, and secondly, that it 
bases a stronger conviction upon a weaker one, a higher 
probability upon a lower one. Granted, if you will, that 
Induction itself, a rude Induction, gradually leads us to be- 
lieve in rigorous scientific Induction ; this may explain the 
genesis of the phenomenon, or how it was that we were 
first led to employ this organon of discovery. But before 
we can accept the fruit of the Induction with the strong 
and unhesitating conviction which we now accord to any 
well-established Law of Nature, we must not only know 
how we were first induced to believe that such a Law 
exists, but we must find some valid principle which may 
fairly be accounted a proof of its existence. Certainly such 
proof cannot be obtained by reasoning in a circle. Mill 
and Comte would have us believe, that our invincible con- 
viction of the universality of the Law of Gravitation rests 
upon no firmer basis than the opinion, which, indeed, is 
daily gaining ground, and which the progress of mere Phys- 
ical Science evidently tends to confirm, that everything in 
nature is subject to law, so that it takes place by a phys- 
ical necessity, and might be predicted with unerring con- 
fidence, if we had a perfect knowledge of its antecedents. 
" Every event has some invariable and unconditional ante- 
cedent " ; — if we hesitate to admit this proposition in all its 
generality, Mr. Mill thinks we cannot consistently believe 
that all matter gravitates, that oxygen is necessary for the 
support of animal life, or even that fire will burn and water 
drown. "We maintain that the latter propositions are in- 
contestable, while the former, the principle of the miiver- 
sality of law, is merely a hypothetical conclusion, though 
an extremely probable one. Accordingly, to base the lat- 
ter upon the former is to make the superstructure stronger 
than its own foundation. Mr. Mill himself is compelled to 
admit, with respect to one very large class of phenomena, 



INDUCTION AND ANALOGY. 395 

those of the human will, that at least one half of the specu- 
lative world, even in our own day, do not believe in the 
universality of law, or that every event is necessarily de- 
termined by its antecedents. And with regard even to 
physical events, a large and increasing number of philos- 
ophers, among whom are ranked Bishop Berkeley, Dr. 
Samuel Clarke, and Dugald Stewart, hold that none of 
them are subject to law, in the sense of being absolutely 
determined by their physical antecedents, but are the re- 
sults of volition, which is free to modify them at any mo- 
ment. But without adoptmg this theory, he is a bold 
advocate of the perfectibility of Physical Science who will 
maintain that the probability of ultimately discovering that 
phenomena still so apparently irregular and inconstant as 
those of the weather, of health and disease, the countless 
peculiarities of individual plants and animals, and the 
equally numerous idiosjiicrasies of human intellect and 
character, are subject to fixed and definite laws, is so great, 
that we may safely rest upon it all our confidence in the 
physical laws that have already been established ; — that 
tliis probability is the measure and the test of all the cer- 
tauity that has hitherto been obtained in Physical Science. 

Let us examine, then, the only remaining theory, which 
is, that the ultimate Ground of Induction is the Law of 
Causahty, or the judgment that every event must have a 
Cause, — not merely a constant physical antecedent, but an 
efficient Cause. It is only necessary to show, that the Law 
of Causality is readily and naturally explicated into the 
Maxim that nature's course is uniform, so that the abso- 
lute and imperative conviction, which belongs to the for- 
mer as an a priori cognition of the human mind, is trans- 
ferred, by an easy association of ideas, to the latter, though 
not logically belonging to it. 

Take the simplest case of Induction, by which we are 
led to expect that any physical object will always continue 



896 INDUCTION AND ANALOGY. 

to manifest the same qualities that have hitherto been ob- 
served in it, unless it is exposed to some new influences, or 
a new antecedent is brought in. Here the assumption evi- 
dently is, that the qualities of the same thing are perma- 
nent, unless some Cause intervenes to change them ; and 
this assumption is logically certain, for it is an Immediate 
Inference from the Law of Causahty, that no change what- 
ever can take place in anything without a Cause. The 
coin must retain the same attributes which it was recently 
observed to possess, if there has not been some Cause of al- 
teration. This proviso is the source of doubt which must 
always arise when an unquestionable abstract truth is ap- 
plied to real objects or actual events. We never can be 
sure that such a Cause of change has not intervened ; but 
we are morally certain that it has not, if there has been no 
apparent alteration of the circumstances of the case, no 
seeming exposure to new influences. To this extent, then, 
we can safely reason from the past to the future, or from 
some to all, when satisfied that the Classification is correct, 
— that is, that no new occurrence or Efficient Cause has 
destroyed the resemblance of the observed instances to the 
expected ones, or of some to the others. 

The next sort of Induction, though a little more compli- 
cated, is easily resolved into the same Law of Causality. It 
has already been shown that among the other properties 
of any particular substance must be ranked its active and 
passive powers, that is, the changes in other bodies of 
which its proximity has been a constant antecedent, or the 
changes to which it is itself subject when brought into re- 
lation with other substances under different circumstances. 
These active and passive powers, regarded as mere se- 
quences of phenomena, may properly be reduced to the 
preceding head of qualities; they form, as we have seen, 
one class of the attributes of every substance, and, as such, 
enter into the Intension of the Concept which denotes that 



INDUCTION AND ANALOGY. 397 

i?ubstance. In truth, what are called secondary qualities 
are only the powers which bodies possess to excite certain 
sensations in us, when brought into relation with our or- 
gans of sense. And in like manner, the capacity of gold 
to be melted on the application of a sufficient degree of 
heat is an integral part of our complex notion of this sub- 
stance. Powers being nothing but qualities, then, the Law 
of Causality is applicable just as in the former case ; these 
powers must be fixed or constant in their operation, if a 
new Cause has not supervened to alter them. The general 
maxim is one of absolute certainty, but in its application to 
a given case we never can be sure that the proviso in it 
has been rigidly fiilfilled. This doubt must always remain, 
and is usually more serious, and less capable of being re- 
duced by further observation and experiment, as regards 
the powers, than with respect to the other qualities, of bod- 
ies. The circumstances to be observed in order to prevent 
the intrusion of a new antecedent are more numerous and 
complex ; we cannot so easily be assured that the cases are 
strictly parallel. The unexpected presence of a little more 
or less carbon may have diminished the fusibility of the 
metal ; if a large mass of iron be near, the action of the 
magnetic needle is disturbed. 

Still further ; — it is now known that the merely physi- 
cal antecedents and other circumstances are not the Effi- 
cient Cause of the phenomenon, but are believed to be its 
regular concomitants only because their presence, thus far, 
has been invariably followed by the effect. Accordingly, 
whatever assurance we may possess that the outward cir- 
cumstances are unchanged, it is still possible that the real 
Cause may be so far modified that the expected result will 
no longer be produced. The doubt which thus rests upon 
the case cannot be dispelled by any precautions Avhatsoever. 
The cases may be strictly parallel in every visible respect, 
as tested by the nicest observations ; but if the physical 



398 INDUCTION AND ANALOGY. 

antecedent was only the occasion, and not the Cause, the 
phenomenon may not be repeated, as it is always possible 
that the true Cause may now for the first time exist under 
different combinations. To recur to the illustration taken 
from Mr. Babbage's machine ; — though, in countless in- 
stances, each number presented has been greater than its 
immediate predecessor by unity, yet as this constant pre- 
cursor was not the true Cause which determined the num- 
ber that was to come after it, it is always conceivable that 
the next presentation should be of an entirely novel char- 
acter. 

We can now see why it is that the Maxim which is the 
Ground of Induction, and on the assumption of which the 
validity of all our reasoning about real objects and actual 
events depends, appears so unquestionably true that we 
regard it as an Axiom. To say that nature's course is 
uniform, and that all events are subject to law, is only to 
assert our intuitive conviction, that every phenomenon must 
have an Efficient Cause, that, while the Cause remains 
the same, the effect must be constant and proportional to it, 
and hence, that, whenever the true Cause is discovered, we 
are enabled to predict unerringly the recurrence of the 
effect. The relation between a true Cause — that is, an 
efficient Cause — and its effect, is radically unlike that be- 
tween a physical antecedent and its physical consequent. 
No absolute conviction, no law of the human mind, mani- 
festing itself anterior to all experience, and thereby first 
rendering experience possible, asserts any connection be- 
tween antecedent and consequent like that which exists 
between Cause and effect. The relation between the two 
former, that of mere succession in time, is contingent, rest- 
ing solely upon experience, and hable to be overturned at 
any moment by subsequent experience ; between the two 
latter, it is a Causal relation, and, as such, is absolute and 
unchangeable, for it is irreversible even in thought. What 



INDUCTION AND ANALOGY. 399 

do we mean when, as a ground of reasoning from some to 
all, we assert that nature acts uniformly, or that all phys- 
ical events are subject to law ? Not, surely, that a given 
antecedent must always be followed by that particular phe- 
nomenon which, according to all experience thus far, has 
been its invariable consequent. This is the only conclu- 
sion which mere Induction aims to establish ; but it is not 
competent to serve as the Ground of Induction itself, or as 
that Premise which must be taken for granted before rea- 
soning by Induction is possible. But we mean only that 
the sequence in question is necessary, if the antecedent is 
the Efficient Cause (or the invariable concomitant, sign, or 
precursor of such Cause) of the consequent. We mean 
only to assert the existence of an irreversible law, and not 
necessarily that such law has already been discovered. 
Comte and all his followers will tell us that no event, how- 
ever extraordinary and unexpected, is to be deemed a 
miracle, — that is, a violation of law, — because the pre- 
sumption is, that further research will either reveal a new 
law, or an improved expression of an old one, under which 
the occurrence, however strange and marvellous, may nat- 
urally be subsumed. He will say, — to adopt a well-worn 
illustration, — that the conversion of water into a solid was 
a miracle to the King of Siam ; but with our larger expe- 
rience, it is no miracle to us, for we have even discovered 
the law, — that is, the constant antecedent, — under which 
the formation of ice takes place. What is this but to assert 
that our conviction of the universality and permanence of 
law, so far from being derived from experience, so far from 
resting on that very process of Induction of which it is the 
sole support, is strong enough to contradict all experience, 
and to maintain its place as an Axiom, though contradicted 
by the largest and most cautious Induction which human 
science has ever framed ? Not even the resurrection of a 
dead man, says the Positivist, would be a violation of 



400 - INDUCTION AND ANALOGY. 

law ; — then his conviction of the permanence of nature's 
laws overrides all the evidence of experience, and contra- 
dicts the whole tenor of modern Inductive science. 

What is called physical necessity is nothing but a convic- 
tion that the relation of an Efficient Cause to its ejffect is 
unalterable, coupled with the assumption, which is a natural 
one, but still illogical, either that the particular antecedent 
or concomitant phenomenon is itself the Cause, or is so 
closely connected with it that its presence must always be 
followed by the recurrence of the effect. The only ground 
of this assumption is the mvariability of the succession in 
time, or the fact that, so far as our experience, or as all 
human experience, has extended, the one phenomenon has 
always been the immediate consequent of the other. That 
this ground is insufficient to justify us in calling the succes- 
sion a necessary one has already been abundantly proved. 
The Positivists, in their desire to eliminate the notion of 
cause altogether, although they are compelled to retain the 
word and all the associations connected with it, refuse to 
attribute the phenomenon to any single antecedent. The 
invariable sequence, they say, exists between a consequent 
and the sum of its several antecedents, all of which must 
concur before we can be sure of the presence of the effect. 
In other words, what they call a cause is only an assem- 
blage of the conditions, all of which must be fulfilled before 
the phenomenon can be reproduced. " The real Cause," 
says Mr. Mill, " is the whole of these antecedents ; and we 
have, philosophically speaking, no right to give the name 
of cause to one of them, exclusively of the others," And 
again, " the Cause is the sum total of the Conditions, posi- 
tive and negative, taken together ; the whole of the con- 
tingencies of every description, which, being realized, the 
consequent invariably follows." Among these " negative " 
conditions, or rather, as the sum of them, he raiks " the 
absence of preventing or counteracting Causes." In con- 



INDUCTION AND ANALOGY. 401 

formity with this view, the distinction between agent and 
vatient, between something which acts and some other 
thing which is acted upon, is formally abohshed, as it is 
denied that there is any action in the case. An inevital)le 
corollary of this doctrine is, that there is no power or effi- 
ciency in any one of the antecedents the exertion of which 
necessarily creates the effect. Yet the denial of any such 
causal agency entirely refutes the hypothesis that there 
is any necessary connection between the two events, and 
leaves their union merely a contingent one, Hable to be 
dissolved or contradicted by subsequent experience. By 
rejecting the doctrine of Efficient Causation, the Positivist 
theory throws away all evidence of the permanence and 
universality of nature's laws. 

This conclusion will appear still more obvious when it is 
demonstrated, as can very easily be done, that every pro- 
cess of Inductive Reasoning, however rigidly conducted, 
and however verified by subsequent observations, is still re- 
solvable, in the last analysis, into the despised " Induction 
by simple enumeration," which Lord Bacon calls mera pal- 
patio, or groping in the dark. The best evidence which 
physical science has been able to collect in support of the 
most generally recognized Laws of Nature amounts only to 
this, that they are found to be true in every instance that 
we happen to know of. Mr. Mill admits that Induction 
necessarily commences with this very imperfect evidence ; 
and he should have added, that it also proceeds and ends 
with it, fiudmo; no other or stronger basis on which to rest 
its conclusions. 

Nearly all the additional evidence which the advance- 
ment of science procures for those conclusions which were 
at first avowedly accepted as inferences from Induction by 
simple enumeration, (perhaps from an enumeration only of 
a few instances, or even from a single case,) arises either 
from extended observation and experiment, from an im- 



402 INDUCTION AND ANALOGY. 

proved classification of the objects about which we reason, 
or from what Dr. Whewell calls, by a happily invented 
phrase, the consilience of several Inductions. The process 
of Induction, when considered as an operation of mind, or 
as a sort of inference, is essentially one and the same, and 
perfectly determinate in character. There are not several 
kinds of it, though there are various degrees of caution, 
precision, and thoroughness with which it is carried out. 
It is always employed with reference to a class of objects, 
qualities, or events, whether that class be well or ill foniied, 
that is, whether the members of it do, or do not, agree 
with each other in all material respects ; and it always pro- 
ceeds from so7ne to all of that class, whether the conclusion 
thus formed does, or does not, coincide or harmonize with 
other conclusions obtained by a perfectly similar process, 
though from other data, and with a different purpose in 
view. The village matron, undertaking to prescribe for 
the illness of her neighbor's child from what she judges to 
be the similar cases that have happened in her own family, 
and Sir Humphry Davy, anticipating that his mode of 
analyzing potash into the oxide of a new metal would not 
only hold good of all other lumps of potash besides the 
very one he was experimenting upon, but would be found 
practicable, and would lead to similar results, in the case 
of other alkalis and earths, are both alike reasoning from 
Induction by simple enumeration. The only difference is, 
that the diseases which affect the human frame are very 
numerous, and, as they have but few recognizable symp- 
toms, can be but imperfectly classified at best, and a village 
matron would probably classify them very ill, so that her 
inference from some to all would be wrong ; while the 
alkalis are few in number, and have determinable and 
strongly marked common qualities, so that the correspond- 
ing inference in their case was entirely safe. 

Attempts have been made at various times to frame what 



raDUCTION AND ANALOGY. 403 

may be called a " Logic of Induction," or a full analysis 
and description of the operations by which we proceed to 
the discovery of physical laws. Lord Bacon, who made 
the earliest and most remarkable endeavor of this sort, 
hoped to furnish a method of scientific investigation which 
should be so complete and accurate as to constitute an or- 
ganon of discovery, and reduce all intellects to a level, 
making success in the search after truth a matter merely 
of time and labor. Taught by experience that discoveries 
cannot be thus made by rule, but are generally the results 
of a tentative process many times repeated, and a happy 
combination of circumstances, the later followers of Lord 
Bacon have attempted merely to analyze and describe the 
process by which discoveries have been made, without hop- 
ing to indicate any sure method of adding to their number. 
But even this endeavor, though aided by all the lights of 
modem physical science, and prosecuted by such eminent 
thinkers as Sir John Herschel, Dr. Whewell, and Mr. J. 
S. Mill, has had but very limited success. The results do 
not agree ; though the same compound phenomena are pre- 
sented for examination, they are analyzed by these three in- 
quirers into very different elements and processes of thought. 
These theorists do not even hold the same opinion as to 
the nature of the process which they have to separate into 
its elements, or, in other words, as to what constitutes In- 
duction. Dr. Whewell, fearful of resting the whole cer- 
tainty of physical science upon so narrow and unstable a 
basis as reasoning in respect merely to all the cases that we 
happen to know of, boldly restricts the name of Induction 
to what seems to be a mere generalization of the facts 
already observed, but as now seen under a new light be- 
cause succinctly comprehended in one general formula ; 
and appears to lose sight altogether of the necessity, if 
science is to fulfil its office of anticipation and prediction, 
of extending the generalization to all the objects and events 



404 INDUCTION AND ANALOGY. 

of a given class, whether they have yet been observed or 
not. Mr. J. S. Mill, who has more confidence in the pre- 
cautions and the means of verification by which men of 
science test and confirm the rude Inductions of the vulgar, 
justly asserts that Dr. Whe well's mere " Colligation of 
Facts," far fi'om being the type of Induction generally, 
"is not Induction at all," but only a new description of 
the phenomena. He undertakes to analyze and reduce to 
system these precautions and means of subsequent verifi- 
cation, and to show that, when they, are duly observed 
and practised, scientific Induction differs in kind, and not 
merely in degree, from Induction by simple enumeration, 
and, though based merely on experience, estabhshes its 
conclusions with the highest certainty of which the human 
mind is capable. But experience, from its very nature, 
cannot extend beyond a limited number of cases ; and as 
even the most cautious and rigorous Induction avowedly 
has no other foundation than experience, either the abso- 
lute universality of the Laws of Nature is not scientifically 
established, or it must be deduced from a priori considera- 
tions respecting the relation of an Efficient Cause to its 
effects. The consilience of several Inductions merely ex- 
tends the enumeration to a larger number of cases; but 
any such extension, of course, cannot include future in- 
stances, nor in any way enlarge the domain of possible ex- 
perience. In fact, most of the scientific processes, which 
are ably analyzed by Mr. Mill, have reference to the use of 
Induction as an organon of discovery, and not as a medium 
of proof; they point out the inferences which we ought to 
make, but they do not render any more stable the founda- 
tion by which all such inferences are supported. And any 
improvements in the modes of observation, or in the classi- 
fication of the things observed, are merely preparatory to 
the process of Induction, and do not in any way affect the 
essential nature of that process. 



INDUCTION AND ANALOGY. 405 

Putting aside the terminology invented by Dr. Whewell, 
and also that recommended by Mr. Mill, as not even their 
authority has sufficed to bring either into common use, it 
may be said that there are but three phrases generally em- 
ployed to designate those results of Induction which con- 
stitute the highest generalizations of science. These are 
a General Fact, a Laiv of Nature, and a Cause, this last 
being now usually miderstood to mean nothing more than 
an Invariable Antecedent. Unfortunately, even these three 
phrases are so wavering and uncertain in their significa- 
tion, that they are often employed as synonymes, while 
hardly any scientific person is consistent in the use which 
he makes of them, and no two writers upon the philosophy 
of the physical sciences agree with each other in the at- 
tempt to limit and define their meaning. 

The first of the number, a General Fact, though em- 
ployed with somewhat more precision and consistency than 
the other two, is yet of narrow and indeterminate range, 
and is grudgingly used, because it is modest in pretension, 
and does not feed the pride of science, or gratify the van- 
ity of the inquirer into the secrets of nature. It coincides 
with what Mr. Mill calls an Empirical Law, or the result 
of an Induction by simple enumeration. Thus, it is prop- 
erly a General Fact that all horned animals are ruminant, 
that all quadrupeds are viviparous, that every living thing 
is pi'oduced from an egg, that opium and alcohol intoxicate, 
&c. But the phrase is sparingly used, because we are not 
content simply to point out a new characteristic of a whole 
class of objects, or to form a new class of facts by tracing 
their hitherto unsuspected agreement with each other, so 
far as our observation has extended, in some latent attri- 
bute. We aspire to the much higher praise of determin- 
ing a new " Law of Nature," which must hold true on all 
occasions, whether observed or not, and the discovery of 
which is therefore equivalent to a revelation of another of 



406 INDUCTION AND ANALOGY. 

tlie imimitable purposes of the Almighty. The General 
Fact is admitted to be true only so far as our observation 
has extended, or at any rate to afford comparatively but a 
slight presumption that it will be found to hold good in 
cases as yet unobserved. But as already remarked, the 
narrower and the more definite the class, the stronger is 
this presumption. Thus, that every antelope is ruminant, 
is a far more probable conclusion than that all horned ani- 
mals are ruminant; we admit very readily that all the 
mammalia are produced from eggs, but not so readily that 
the whole animal kingdom are thus produced. 

A Law of Nature, in its more definite signification, is 
employed to designate a group or series of General Facts, 
relating to the same subject or class of subjects, and differ- 
ing from each other by some mode of proportional varia- 
tion, so that the place of every member of the series may 
be easily deduced fi-om one numerical formula. Such are 
Kepler's laws of the planetary motions, the law of definite, 
reciprocal, and multiple proportions in Chemistry, and of 
phyllotaxis in Botany. The General Facts may be known, 
long before their relation to each other, or their law of 
proportional variation, is discovered. Thus, the General 
Fact that the leaves of the apple-tree are disposed in cycles 
of fives, and so that the spiral line connecting their points 
of insertion passes twice round the stem for each cycle, 
their arrangement being thus conveniently denoted by the 
fraction |, was ascertained, and a corresponding General 
Fact for many other species of plants was equally well 
known, before the " Law " was discovered, that the result- 
ing fractions fall into a series, any one of which has for its 
numerator the sum of the two preceding numerators, and 
for its denominator the sum of the two preceding denomi- 
nators. So, also, the General Facts in Optics, that the 
angle of refraction, measured from the perpendicular to 
the surface of any medium heavier than air, is always less 



INDUCTION AND ANALOGY. 407 

than the angle of incidence, and is not proportional to it, 
were commonly known, and even Tables had been labori- 
ously formed, giving experimental measures of refraction 
for the various angles of incidence, and for different media, 
many centuries before Snell, in 1621, superseded the use 
of many of these Tables by discovering the simple Law 
of Nature, that the ratio of the sines of the angles of 
incidence and those of refraction is constant for the 
same medium. Every measurement of refraction as for- 
merly given in those Tables w^as a General Fact, includ- 
ing every case of a ray of hght falling upon the given 
medium at the given angle ; and this Fact was obtained, 
of course, by reasoning Inductively, that as the refraction 
for this angle of incidence and this medium had been ac- 
tually observed to be of this magnitude in some cases, 
(namely, in all that had been observed,) it would be 
found of the same magnitude in all such cases. Snell's 
discovery of the " Law " took the place of an immense 
number of such Facts, by summing them all up in one 
general proposition or formula, thereby rendering any de- 
tailed mention of them unnecessary. 

Such a discovery as this by Snell is what Dr. Whewell, 
by a happily selected phrase, calls a " Colligation of Facts " ; 
and the process by which it is arrived at — the method, if 
there be one, of making such a discovery — is what he de- 
nominates Liduction. Mr. Mill very properly objects, that 
it is not Induction at all. It is an act of generalization, 
founded on direct intuition of the relations which the cases 
actually before us bear to each other, and not professing to 
extend beyond these cases. Consequently, it does not en- 
large our knowledge, as Induction always does, but only 
grasps up together into one Concept the knowledge which 
we already possessed ; and it accomplishes this through 
perceiving that this group of General Facts, instead of 
being entirely heterogeneous, as they at first appeared, 



408 INDUCTION AND ANALOGY. 

are really linked together by some common relation, the 
expression of which reduces them to unity in the Under- 
standing, and so renders them more easy to be remem- 
bered and more convenient to be used. 

It is true, as Mr. Mill remarks, that a real act of Induc- 
tion usually goes along with the Colligation, as subsidiary 
to it. In this case, Snell not only took for granted the 
previous Inductions, which, as we have seen, are expressed 
m the separate General Facts that he grouped together in 
his formula, but also, having ascertained by actual observa- 
tion that this formula held true for refraction in some media, 
he reasoned Inductively that it would hold true for all 
media, or, in other words, that it was the universal Law 
of refraction. 

It ought also to be remarked, that the discovery of the 
Law which colligates the General Facts does not change 
the nature of the evidence on which those Facts depends, 
or raise them out of the rank of Probable, into that of De- 
monstrative, judgments. These Facts are still nothing but 
truths of Induction, just as much after the discovery of the 
Law as they were before it. The discovery, it is true, 
makes the previous Inductions somewhat more probable 
than they were before ; but it does not by any means de- 
monstrate them. The degree of probability is increased 
through the discovered eovisilience of the Inductions, as this 
consilience amounts to increasing the basis of enumera- 
tion on which each of them rests. A number of conclu- 
sions affecting a group of kindred subjects are mutually 
sti'engthened, when it is found that the separate Induction 
leading to each one of them harmonizes in one respect, 
or in several respects, with the Inductions leading to all 
the others ; for such harmony is precisely what we expect, 
in view of the Maxim on which all Inductive reasoning; 
depends, that nature's course is uniform. Each Induction 
stands more fii'mly, when it not only rests on its own foun- 



V 



INDUCTION AND ANALOGY. 409 

dation, but is indirectly supported by the foundations of its 
neighbors. 

According to the view here given, a Law of Nature is a 
generalization of the second order ; in some respects, it 
bears the same relation to General Facts, that a General 
Fact bears to Individual Facts. I say "in some respects"; 
for this statement does not convey the whole truth. A 
Law of Nature is not a mere ti'uth of classification ; it is 
not merely a Genus of which the several General Facts are 
the Species. If it were, then the tabulated measures of 
refraction, or any other mere collection of General Facts 
relating to the same class of subjects, might be called a 
Law. But it is not so ; a Law may be contained in such 
a Table, but it is concealed there, and when discovered, 
the Table itself becomes useless. The discovery, as I have 
said, consists in a perception of the truth, that the group 
of General Facts falls naturally into a series, in which the 
place or power of any term is easily deduced from a single 
brief formula. The effort of mind by which such a dis- 
covery is made is rather an Intuition, or a happy conjec- 
ture, than an Induction. The kind of conviction which 
attends the discovery, when made, is not mere probability, 
but certainty. With reference to the General Facts actu- 
ally before us, we know that the Law is there, for we see it 
just as soon as we have learned where to look for it. But 
the universality of the Law, the extension of it to all other 
General Facts, not now observed, of the same class, is the 
result of an Induction ; and the establishment of the Law 
also takes for granted the validity of the preceding Induc- 
tions on which each separate General Fact depends. Hei'e, 
as elsewhere, whenever we attempt to extend our knowl- 
edge beyond what is actually observed, our only guide is 
Induction by simple enumeration. 

The process of hvinting for a Law of Nature amid a 
group of General Facts is essentially tentative, resembhng 

18 



410 INDUCTION AND ANALOGY. 

an attempt to find the meaning of a riddle ; we try one 
guess after another, and at last stumble upon the right one 
when we least expected it. Success is usually obtained, 
not by trying to extend the survey, or to contemplate the 
largest possible number of cases, but by restricting the 
field of search to a few well-chosen instances, and attempt- 
ing to find a pattern or construction which these few will 
precisely fit. To take an example from a quarter where 
we should least expect to find one, — from pure mathe- 
matics ; Newton discovered the Binomial Theorem, which 
is a true Law of Nature according to our definition, prob- 
ably by simple inspection of a few of the loAver powers of 
binomials, the law of the exponents being obvious enough, 
and that of the coefficients offering but little difficulty to 
his marvellous insight. He certainly discovered and used 
the Theorem long before he endeavored to demonstrate it, 
or to trace it to its true mathematical principles. There 
is reason to believe that not a few of the general theorems 
of the higher mathematics have been discovered in a pre- 
cisely similar manner. 

Why the Law should be suddenly revealed to a single 
happy glance, when it had previously escaped the most 
laborious research, is a curious problem, which perhaps 
admits of no complete solution, though the process may 
be elucidated in a few particulars. The essential charac- 
teristic of such a Law is a series proceeding by some uni- 
form gi'adation, the relation between two or more consecu- 
tive terms in any part of it being the same as that existing 
between the corresponding terms in any other part. This 
relation may be simple or complex, recondite or obvious. 
Each term may be an increment of its predecessor by the 
addition of a constant quantity, or may be a simple multi- 
ple of it, or may be related to it through some of the peri- 
odic magnitudes connected with a varying angle, such as 
the sine, tangent, secant, &c. ; or the law of progression 



INDUCTION AND ANALOGY. 411. 

may be covered up, as it were, by a constant quantity 
added to each of tlie terms ; or the numbers, as we have 
them, may be tlie complex results of two or more indepen- 
dent series multiplied into each other, in which case there 
are two or more independent Laws to be discovered. Two 
difficulties, then, are to be overcome, either one of which 
would seem to be insuperable if the other had not been 
previously mastered ; we must properly aiTange the terms 
of the series before the Law of it can be discovered, but a 
knowledge of the Law is indispensable before we can with 
certainty make such an arrangement. In a contest with 
so many and so serious difficulties, it is not surprising that 
success at last should often seem attributable quite as much 
to accident, as to sagacity and dogged perseverance. 

Kepler has furnished an instnictive narrative of his suc- 
cessive attempts to reduce to Law the astronomical obser- 
vations of Tycho, constructing many formulae by hypothesis, 
finding that one after another would not fit, and, after each 
disappointment, trying again with unwearied patience. At 
last, his perseverance was rewarded with the discovery of 
the great Laws which deservedly bear his name, as they 
are the foundations of the whole modern science of astron- 
omy, for they sum up in three sentences all recorded as- 
tronomical observations. He also attempted, in a similar 
way, to detect the Law concealed in the measured angles 
of refi'action, by comparing them with the angles of inci- 
dence through a variety of constructions by triangles, conic 
sections, &c. ; but all without success. Where he failed, 
Snell succeeded, twenty years later, merely by turning his 
attention from the direct measures of the angles to the ratio 
of their sines. The law was then manifest at a glance. 
Such instances are needed to remind us, that the well- 
known fable of Columbus and the egg is not a caricature, 
but a faithful representation, of many of the greatest dis- 
coveries in science. What Dr. Whewell happily calls 



412 INDUCTION AND ANALOGY. 

" the ex-post-facto obviousness of discoveries, is a delusion 
to which we are hable with regard to many of the most 
important discoveries." 

The vahdity of a Law of Nature thus discovered, as it 
were, by a happy casualty, is regarded as sufficiently estab- 
lished by comparison with but very few of the observed 
data from which it was educed. Thus, Dalton's magnifi- 
cent generalization, coextensive with all matter, and now 
verified by almost countless analyses, that chemical ele- 
ments combine only in definite, reciprocal, and multiple 
proportions, was first suggested to him during his examina- 
tion of onl}'- two compoimds ; " and was asserted gener- 
ally," says Dr. Whewell, " on the strength of a few facts, 
being, as it were, irresistibly recommended by the clear- 
ness and simplicity which the notion possessed." What is 
the ground of this bold anticipation of the universality of a 
Law as yet verified only by a very few examples, when, in 
the case of a General Fact, as already shown, a very ex- 
tensive Induction may still leave us in doubt whether the 
supposed truth may not be contradicted by the next in- 
stance that arises ? In general terms, the answer is obvi- 
ous. Simple uniformities, such as are comprehended in a 
General Fact, may be merely accidental ; to recur to an 
instance already cited, all ruminating animals now known 
divide the hoof; b\it as the number of such animals is not 
very great, this simple coincidence of two properties may 
be as casual as the experience of an individual observer 
who has never happened to see a squint-eyed person that 
had not also brown hair. But complex uniformities, such 
as are marshalled into the symmetrical series called Laws 
of Nature, and tlius expressed in one formula, cannot be 
regarded as accidental. As tlie number of individual facts 
comprehended in one of these series is very great, it is in- 
credible that mere chance should throw even a portion of 
them into symmetrical groups, bearing a constant ratio to 



INDUCTION AND ANALOGY. 413 

each other. Hence, if we can detect but a portion, even a 
fragment, of such a series, we feel assured that it will prove 
to be continuous, that the Law will not change, that the 
uniformity will be carried out to the end. Only the action 
of a permanent and unvaiying Cause, it is assumed, could 
so harmonize results. Nay, so strong is our assurance of 
the universality of the principle thus discovered, though it 
seems as yet very imperfectly verified, that, when an anom- 
alous or inconformable instance actually arises, we seek at 
once for the means of eliminating it, or explaining it away, 
instead of allowing it to wrest the inchoate discovery out 
of our grasp and send us to the work of research again. 
We class the exception immediately among those apparent 
exceptions which really confirm the rule ; — just as we 
now see that the rising of a balloon in the atmosphere does 
not contradict, but actually verifies, the Law of gravita- 
tion. 

We come, then, to the conception of a physical Cause, as 
indicating the third or highest stage in the generalizations 
of science, and therefore as bearing the same relation to a 
Law of Nature, that such a Law bears to a General Fact. 
As thus understood, a Cause is simply a higher Law, un- 
der which several inferior Laws are subsumed ; it appears 
as the original principle, of which these lower Laws are 
the derivatives by immediate and necessary consequence. 
Thus, the theory of gravitation, or the doctrine that every 
body attracts every other body with a force which is di- 
rectly as its mass and inversely as the square of its dis- 
tance, is the statement of a universal principle, under which 
not only Kepler's Laws of the planetary motions, but the 
Laws of falling bodies, of the equilibrium of fluids, &c., are 
subsumed in this sense ; — that if we take for gi'anted the 
existence of the force or physical Cause, termed Gravity^ 
which this theory assumes, then these inferior Laws may 
all be deduced from it by Demonstrative Reasoning. That 



414 INDUCTION AND ANALOGY. 

such Deduction is possible, is the only proof we have that 
such a force or Cause exists. The hypothetical force, for it 
is nothing more, represents the inferior Laws that are sub- 
sumed under it, merely because it is an expression of them 
in a single formula. It may well happen that two or more 
such formulas may be devised, differing essentially from 
each other, yet answering equally well all the conditions 
of the case, as the given Laws may logically be deduced 
from either of them. For instance : — all, or the greater 
part, of the Laws of vision and light may be explained with 
equal precision and accuracy either on the doctrine of emis- 
sion, or on the undulatory theory. Two such hypotheses 
correspond to two very dissimilar engines, which different 
mechanics might invent, in order to cause the hands of a 
clock to make the required movements over the dial-plate, 
or the little balls in an orrery to counterfeit the motions of 
the solar system. It is no more necessary to suppose that 
such an attractive force as Gravity, or such a luminiferous 
ether as the undulatory theory treats of, actually exists, 
than it is to believe that a set of wheels and pinions, like 
that which moves an orrery, really produces the motion of 
the planets. All that the theory does for us is to represent 
the phenomena correctly; no one who understands the 
subject supposes that the hypothetical force or Cause, which 
is merely a convenient supposition for the theorist, actually 
produces those phenomena. 

It is evident that such Causes as we are now speaking 
of are merely the highest generalizations of Physical Sci- 
ence, and that the invention of them — for they are rather 
invented than discovered — affords not the slio;htest addi- 
tional evidence of the universality of those Laws of Nature 
which they represent, or which are subsumed under them. 
The proof, indeed, proceeds in the opposite direction ; the 
only evidence we have that the right Cause has been as- 
signed is, that it correctly represents the Laws which are 



X. 



INDUCTION AND ANALOGY. 415 

placed under it. When it is demonstrated that the Law 
may be deduced from such a Cause, the real course of the 
argument is, from the admitted validity of the Conclusion 
to infer the soundness of the Premise. Gravity does not 
cause heavy bodies to fall to the ground, nor does it bind 
the planets to their orbits ; but Gravity is rightly consid- 
ered as a " physical Cause," in the technical sense of that 
phrase, because its hypothetical existence enables us cor- 
rectly to represent in a single formula the phenomena of 
falling bodies and of the planetary motions. 

The higher generalizations, then, depend exclusively, for 
proof of their correctness, on the validity of those which are 
next below them. When the proper Law of Nature is 
provisionally assumed, certain consequences can be demon- 
strated to follow which acrree with the General Facts that 
were previously established on Inductive evidence ; when 
the proper physical Cause is assumed, we can logically 
make certain Deductions from it which harmonize with the 
Laws of Nature which this Cause was invented to express. 
Neither the Law nor the Cause brings any additional evi- 
dence of its own, but both alike depend for proof, in the 
last analysis, on the validity of the Induction by simple 
enumeration by which we first collected their common 
basis, the General Facts. The process of verifying both 
consists in enlarging the Induction, but not in altering its 
character ; both the Law and the Cause being assumed to 
be universally true, we make ftirther Deductions from 
them, and still find these to coincide with the observed 
Facts. In other words, we first reasop Inductively from 
some to all, and then, assuming provisionally that the prin- 
ciple holds true of all, we reason from it Deductively to 
other some, and find that these also are confirmed by obser- 
vation, so that they reflect evidence upon the Law or the 
Cause of which they are the logical consequences. Turn 
the matter as we may, Induction by simple enumeration is 



416 INDUCTION AND ANALOGY. 

still the basis of the whole procedure, and the discoveiy or 
invention of Laws of Nature, or physical Causes, only sup- 
plies names and formulas of expi-ession for the successive 
steps of generalization, as we form one after another the 
proper hierarchy of Concepts. 

We can now see more plainly than before the correct- 
ness of the doctrine already advanced, that the strong and 
inhesitating belief which we accord to any well-established 
Law of Nature, and which we indicate by saying that an 
event happening under it takes place by a physical neces- 
sity^ is not due to the strength of the Induction through 
which the Law was discovered, but to our absolute a 'priori 
conviction of the fixedness of the relation which connects 
every effect with its efficient Cause. The Law is discovered 
by Induction ; but it is proved by a different process, — by 
bringing it under a necessary a priori conception of the 
human mind, that of Efficient Cause, and thereby subject- 
ing it to the principle of Causality, that every event must 
have a Cause, and must be proportional to that Cause. 

In speaking of the use which is sometimes made of In- 
ductive reasoning in pure mathematics, as in the case of 
Newton's discovery of the Binomial Theorem, Mr. Mill 
maintains that the process of thought in such cases is not 
an Induction properly so called, but is governed by certain 
" a priori considerations (which might be exhibited in the 
form of demonstration), that the mode of formation of the 
subsequent terms, each fi.'om that which preceded it, must 
he similar to the formation of the terms which have been 
already calculated^" But it was certainly Inductive in this 
respect, that the observed regular formation of the first few 
terms of the series originally led Newton to anticipate that 
all the other terms must be formed hi the same manner, 
and to act upon this anticipation, — that is, confidently to 
use the Theorem for a long time, — without giving himself 
the trouble to work out a demonstration of it. Undoubt- 



INDUCTION AND ANALOGY. 417 

edij he had a strong belief that such a demonstration was 
practicable ; and this belief prompted him to acquiesce with 
greater confidence in the result of the Induction. For this 
very reason, this instance appears to be a typical and in- 
structive case of Inductive reasoning. Pure Induction is 
exclusively an organon of discovery, a clew for anticipating 
facts not yet observed and truths not yet proved. The 
Ground of the Induction, that is, the proof, if it may be 
called such, or the source of the confidence with which we 
accept its conclusions, is an indistinct assurance, derived 
from a priori considerations, that the results might be de- 
monstrated, if we were acquainted with all the circumstances 
of the case. Newton's assurance was founded on his indis- 
tinct anticipation of the truth, that the formation of the co- 
efficients of the series must depend in some manner on the 
laws of the permutation and combination of numbers, — 
an anticipation which he did not stop to work out and 
verify. The physicist's assurance is based primarily, as 
we have seen, on his necessary conviction that every event 
or change must have an efficient Cause, a truth which 
is readily explicated into the maxim that Natm-e's course 
is uniforaa ; and secondarily, upon his belief that the pro- 
portional variation of the successive terms in such a se- 
ries as is called a Law of Nature is another consequence 
of the axiomatic principle of Causality, that effects must be 
proportional to their Causes. The physicist's anticipation 
cannot be verified, because, in the physical universe, Effi- 
cient Causes lie beyond the reach of human insight. We 
can discover nothing but Invariable Antecedents. But so 
strong is the bias which leads us to identify an Invariable 
Antecedent with an Efficient Cause, that the phraseology 
of Causation is still employed throughout our investigations, 
though it has been demonstrated over and over agam, that 
constancy of sequence is no certain indication of causal 
efficiency. We still speak of physical Causes, of agents 

18* AA 



1 



418 INDUCTION AND ANALOGY. 

and their action, o{ forces and potvers, altliougli it is now 
admitted on all hands that we mean nothing by such 
language, when employed with reference to the material 
universe, except "constant relations of succession or of 
similarity." The very persistency of this inappropriate 
phraseology indicates quite clearly the source of our con- 
viction that Nature's course is uniform, and her Laws un- 
changeable, except by Him whose infinite wisdom first 
established them, and whose unvarying purposes and modes 
of action they express. 



SOURCES OF EVIDENCE AND CAUSES OF ERROR. 419 



CHAPTER XIII. 

THE SOURCES OF EVIDENCE AND THE CAUSES OF ERROR. 

INTUITION is not only the source in which all our 
knowledge originates, but it is the universal basis of 
certainty, or the sole ground of the confidence with wliicli 
we accept any facts or truths as known. What we directly 
or immediately perceive, whether by the external senses 
or by consciousness, that we know. What is not thus di- 
rectly perceived is entitled to be called knowledge only in a 
secondary or derivative sense ; properly speaking, it is only 
an inference from our knowledge, and however legitimate 
this Inference may be, it is worth nothing if the truth of 
one or more Intuitions, on which it depends, be not previ- 
ously taken for granted. Take even Demonstrative Rea- 
soning, for instance, in which it is rightly said that the 
Conclusion is a necessary inference from the Premises. 
Still, before we can accept this Conclusion as certain, we 
must assume that both the Premises are true. Now, what- 
ever be the nature of the Major Premise, the Subsumption 
must express, either directly or indirectly, a truth of Intui- 
tion. We can knowingly assert that a given object pos- 
sesses a certain attribute, or bears a certain relation of like- 
ness or unlikeness to some other object, only through our 
direct perception of this fact either by sense or conscious- 
ness ; and such an assertion must enter into every act of 
Reasoning, as one of the grounds on which the Conclusion 
rests. Any Reasoning, then, by which we might attempt 
to doubt or deny the validity of our Intuitions, would be 



420 THE SOURCES OF EVIDENCE 

self-destructive ; for in such Reasoning, the truthfulness of 
our Intuitive faculties must be presupposed, or taken for 
granted. We should, by such scepticism, deny the legiti- 
macy of our dwn denial. 

Intuition, therefore, is the highest source of evidence, 
and the ultimate foundation of all certainty. If we can- 
not accept, as absolutely true, what we immediately per- 
ceive, or are conscious of, then we can know nothing ; we 
cannot even know that we do not know. But before we 
place this absolute reliance upon Intuition or Perception, 
we must carefully distinguish what it is that we really per- 
ceive, or, in other words, what that is of which we have 
an Intuition. In ordinary mental action. Inferences are so 
quickly and habitually drawn from Intuitions, and thereby 
so closely blended with them, acts of comparison and gen- 
erahzation also entering into the compound result, that it 
becomes extremely difficult to separate the pure Matter of 
Intuition, of which we are absolutely certain, from the 
heterogeneous ingredients which are thus united with it, 
and of which we are not by any means equally sure. 
Hence it is often said that our senses deceive us, when 
the truth is, that we are mistaken only in the Inferences 
which we have incorrectly drawn from the data actually 
furnished by the senses. Thus we are often deceived into 
accepting a counterfeit as a good coin ; but the mental act 
which thus leads us into a mistaken belief is really com- 
pound, embracing an act of memory, one of generaliza- 
tion, and one of Reasoning. The little object placed in 
our hands for examination is perceived to have a certain 
color, weight, shape, stamp, &c. ; and it is impossible that 
these quahties should be, to us, in any respect different from 
what they are perceived to be. But when we proceed to 
compare these qualities with others which we rememher to 
have perceived at some other time in good coins, and to 
infer from their similarity that this supposed coin is not a 



AND THE CAUSES OF ERROR. 421 

counterfeit, it is evident that we are exposed to many 
sources of error. Even if we go so far only as to desig- 
nate one of these qualities by its Common Name, — to say, 
for instance, that this coin is yellow^ — we go beyond the 
Intuition, and, so far, become liable to mistake ; it may well 
be that we have but an imperfect recollection and imagi- 
nation of the color which is usually so called, and therefore 
may be mistaken in supposing that this color is so similar 
to it as to merit the same name. In like manner, any 
other comparison, as of the weight, shape, or stamp, as it 
requires either memory, if both objects be not actually be- 
fore us, or a decision as to the degree of similarity, if they 
are both present to sense, must involve an element of un- 
certainty. 

The question has been raised, whether external objects 
are directly perceived by us as external^ or whether their 
externality is an Inference subsequently drawn from this 
perception as combined with others, and as governed by 
the necessary and a priori convictions of the mind. \\\ 
other words, is the externality of the object, or the fact 
that it is something different from myself, that it is not-me, 
a constituent part of the Intuition, or only an Inference 
from it? If the former supposition be true, then I know 
that the external world exists, and any Reasoning upon the 
case, either for or against this knowledge, is superfluous, 
and even illogical ; for as Reasoning must involve and de- 
pend upon Intuition, it cannot contradict Intuition. But 
if the latter supposition be correct, then the reality of the 
outward universe is not, strictly speaking, knoivn, but only 
inferred through an act of the understanding, which, as it 
purports to relate to real objects, and not to a mere con- 
ception of the mind, certainly may be a mistaken one. 

The question is an important one, but the full discussion 
of it belongs to Metaphysics, and not to Logic. We can 
only consider here the nature and the relevancy of the evi- 



422 



THE SOURCES OF EVIDENCE 



dence adduced, regarded as illustrating the general laws of 
evidence. Thus much, I think, must be admitted, that 
the mind, in its adult state, is immediately conscious of the 
affections of its own bodily organism as such^ — that is, as 
affections of the body, which is foreign to itself, or a part 
of the not-me ; for we localize these affections, or refer them 
instantly, and without an act of reasoning, to the affected 
parts. Thus, I am immediately conscious of a pain, not 
merely as a pain, but as a pain in the foot, in the hand, or 
in the head, the Intuition extending to the locality, just as 
much as to the severity, of the affection. But it is said 
that the pain, being a sensation, can exist only in the sen- 
tient mind, and not in the unsentient matter of the body. 
Very true; but the question then arises, Where is the mind? 
You have no right to confine it to a certain part of the 
body, — to the brain, for instance. I say, that the mind is 
wherever it feels ; for its feeling — its state of consciousness 
— is the only evidence that we have of its existence. It 
is present, at least, to the whole nervous organism. As we 
certainly feel at the tips of our fingers, it is little more than 
tautology to assert, that that which feels is existent at the 
tips of the fingers. It is admitted that this doctrine of the 
ubiquity of the mind to the body is incomprehensible ; we 
cannot see how it is that the thinking being should be " all 
in every part " of its extended nervous organism. In like 
manner, many physical facts, especially those of electricity 
and magnetism, and whatever involves the action of what 
are called Polar Forces, are inconceivable ; but this is no 
reason for doubting their reality, when they are evidenced 
by Intuition. But if the mind immediately localizes its 
sensations, if it perceives that the pain is here, and not 
there, then it is immediately conscious of its own body as 
extended, and therefore of space and externality. 

This is a mere outline of Sir William Hamilton's doc- 
trine of our immediate perception, or consciousness, of the 



AND THE CAUSES OF ERROR. 423 

external world. It appears to disprove very satisfactorily 
Kant's counter assertion, that space is wholly subjective, 
— a mere law of our perceptive faculty, which imposes 
the modes of its own being upon the constitution of the 
objects which it perceives. But while the Hamiltonian 
doctrine seems to hold good of the adult mind, it is not so 
clear that it would apply to the perceptions of an infant. 
It may be questioned whether, at the dawn of our exist- 
ence, our sensations are distinctly referred to outward 
things, or that the perceptions by which they are accom- 
panied appear to be anything else than states of our own 
consciousness. An infant's world, it may be suspected, 
lies entirely within himself; and if so, the subsequent 
reference of these perceptions to external realities must 
be produced, or aided, by experience and an act of Reason- 
ing, and the knowledge or belief thus gained is no longer 
exclusively Intuitive. 

Passing over this metaphysical question, however, it is to 
be observed that Memory, as a source of evidence, stands 
next in extent and importance to Intuition. In many cases, 
the two are so closely interwoven with each other, as we 
have just sfeen, that facts are often loosely said to be Intui- 
tively known, when we have no better evidence of their 
existence than is afforded by Memory. Intuition, as such, 
is always present, relating only to what exists now and 
here; past Intuitions can be now knoAvn to us only by an 
act of remembrance ; and as the strength of a chain is the 
strength of its weakest link, that which we did know Intui- 
tively, can be now accepted only on the strength of our be- 
lief that we remember rightly. In like manner, when we 
are judging of Individual Objects by comparison, or are 
ascertaining their relations to each other, or to a class of 
cognate Objects, the results of the observation will not be 
Intuitively certain, unless all the related objects are pres- 
ent, at one and the same moment, either to sense or con- 



424 THE SOURCES OF EVIDENCE 

sciousness ; if all are not thus present, then, to the extent 
of this deficiency, objects actually observed must be com- 
pared with those which are merely remembered. More- 
over, as Locke and Dugald Stewart have remarked, even 
in mathematical demonstration, we have not, at every step, 
the immediate evidence of Intuition, but only that of 
Memory. The whole science of geometry hangs together 
by a continued chain of Intuitive judgments ; but in the 
case of any advanced theorem, it is not to be supposed that 
we can carry in mind, as simultaneously present to con- 
sciousness, all the truths, previously established, which must 
concur in order to support this particular demonstration. 
In by far the greater number of instances, we trust entirely 
to judgments resting on the evidence of Memory. At the 
close, before we can accept the Conclusion as demonstrated, 
we must remember the whole chain so perfectly as to be 
sure that nothing has been left out ; we must recollect not 
only that we have proved, but how we proved, each point. 
Practically, then, the truths of geometry, and all other 
Conclusions dependent on a chain of Demonstrative Rea- 
soning consisting of more than two or three links, must be 
accepted on the evidence of Memory quite as much as on 
that of Intuition. Of course, the Inductive Sciences, in- 
cluding, as they do, a vast collection of facts, are dependent, 
to a still greater extent, upon this source of evidence. 

But the edifice of Science, when it is thus shown to be 
largely dependent upon individual recollections, would seem 
to rest on a very insecure basis. The defects of Memory, 
as every one is aware, are both numerous and grave. It 
is capricious, it often fails us when we most need its aid, 
and it exists in very different degrees in different persons. 
We might be tempted, at the first glance, to pronounce it 
one of the most untrustworthy of all our faculties. But on 
closer observation, it will appear that the faults with which 
it is chargeable are not so serious as we might at first sup- 



AND THE CAUSES OF ERROR. 425 

pose, and, especially, that they do not much diminish its 
useftilness, or the confidence which we place in it, as an 
indispensable means for the progress of Science. In the 
first place, its faults are rather negative than positive in 
character ; we often forget, but we are very seldom mis- 
taken in what we think that we distinctly remember. In 
truth, a remembrance, seemingly clear and distinct, of 
what we have but recently observed, especially if the phe- 
nomenon be of a simple and definite character, must be 
placed next to Intuition as a ground of certainty. The 
distinction between a pure Intuition now present to the 
mind, and a distinct recollection of a very recent one, ex- 
perienced perhaps within the last hour, is theoretical rather 
than practical. In the ordinary conduct of life, no one 
would think of maintainino; that the former was more trust- 
worthy than the latter. Our judicial tribunals, in grave 
matters involving property and life, will not allow the clear 
and distinct recoUections of a witness, though extending 
over a much longer period, to be even called in question. 
Still, the theoretical distinction exists ; Intuition, as the 
basis of Demonstration, has absolute or logical certainty, 
and does not admit of degrees ; Avhile Memory is confess- 
edly subject to error, and therefore is a source only of 
probable evidence, though, in its highest degree, it amounts 
to what is called moral certainty. 

And here another distinction must be drawn. We must 
distinguish, as Hamilton has done, between the simple fact 
that we do remember, or think that we remember, a cer- 
tain phenomenon, and the truthfulness of this act of re- 
membrance, or our belief in the former actual existence of 
that phenomenon. The former is matter of direct Intui- 
tion, and therefore does not admit of doubt ; the latter rests 
merely upon probable evidence, and may be a mistaken be- 
lief. Memory may be compared to a witness giving testi- 
mony in a court of justice ; the judge and jury cannoi 



426 THE SOURCES OF EVIDENCE 

doubt that he does testify to this or that occurrence, for 
they have sensible — that is, Intuitive — evidence of the 
fact ; but they may well doubt whether he testifies truli/, — 
whether the occurence in question ever took place. It is 
only in this last respect, the correctness of the representa- 
tion of what we remember, that the faculty of Memory is 
said to be a source of merely probable evidence. 

It is to be observed that the art of writing is a most val- 
uable auxiliary to the faculty of Memory, inasmuch as a 
proper use of it may obviate, in great part, the uncertainty 
that would otherwise attach to this source of evidence. 
Remembrance is more perfect, that is, more clear and dis- 
tinct, and thus more trustworthy, according as the Intui- 
tions which it preserves and stores up are more recent. 
But a written record of the observations, taken at the 
time when they were made, or as soon afterwards as might 
be, keeps the evidence as perfect as it would be if Mem- 
ory were not liable to be impaired by the lapse of time. 
The possession of such a record may enable even future 
generations to accept the evidence of the occurrence with 
as full confidence as if it had been observed by their con- 
temporaries only a few days, or a few houi's, before. Of 
course, the age and genuineness of the document mxist first 
be proved, just as we must first establish, on satisfactory 
grounds, the veracity and competency of the witnesses who 
testify to contemporary events which we have not ourselves 
observed. But this being done, and it is generally about 
as easy to do in the one case as in the other, the evidence 
remains as perfect after the lapse of centuries as it was at 
the time when the record was made. Time is thus de- 
prived of its power to wipe out by degrees the recollection 
of events. Many facts in history, though of very old date, 
must be admitted to be now as firmly established as if they 
had taken place within the lifetime of the present genera- 
tion. Thus, the fact that a deed of privileges, called the 



AND THE CAUSES OF ERROR. 427 

Great Charter, was granted by King John to the English 
people, June 5, 1215, is even now as firmly established as 
that of the passage of the Reform Bill in 1832; and the 
precise nature and extent of the franchises gi'anted are as 
fully known in the former case as in the latter, for in both 
cases the original parchment rolls, on Avhich these title- 
deeds of freedom were first engrossed, and attested by the 
seals and signatures of those who were parties to them, are 
yet extant. 

We dwell upon this point as one of some importance, be- 
cause it has been wrongly maintained, in reference to what 
may be called the historical part of Christianity, that as the 
mere lapse of time slowly, but surely, wears away all his- 
torical evidence, the ^eat facts on which our religious faith 
depends must become subject in future centuries to so 
much uncertainty as to be wholly unworthy of credit. 
The proper answer to this assertion is, that nothing less 
than a general conflagration, which should burn up all the 
written and printed records now in existence, could make 
these facts, to any appreciable extent, less certain thousands 
of years hence, than they are at the present day. Miracles 
were needed for the first establishment of Christianity ; but 
only the ordinary course of God's providence is necessary 
to preserve its blessings to any number of future genera- 
tions. 

The two faculties of Intuition and Memory are the 
sources only of our individual experience. But the ex- 
perience of an individual — what I have myself observed 
and remembered, or reduced to writing — is extremely 
limited, when compared with the vast flmd of information 
that is opened to us by accepting the experience of our fel- 
low-men, and combining it with our own. Not merely in 
our labors for the advancement of Science, but in the or- 
dinary management of our every-day concerns, we are 
obliged to depend upon the Testimony and the Authority 



428 THE SOURCES OF EVIDENCE 

of others. Science grows bj a combination of the labors 
of many minds and a long succession of generations. The 
lifetime of an individual might be spent in a vain endeavor 
to review, and verify by personal observation, all the data 
which su})port the conclusions in but one of its depart- 
ments. Many of them, from the nature of the case, can- 
not be so verified; the occurrences of former times, and 
even those in our own day that took place under a pecu- 
liar combination of circumstances, such as may never be 
repeated, must be received on the Testimony of others, or 
be left entirely out of account, together with all the con- 
clusions that are founded upon them. We must contin- 
ually accept on trust what others have observed, and even 
the Inferences that they have drawn, without pretending 
to verify them for ourselves, or we must sit down in igno- 
rance. And this remark is applicable not merely to the 
Inductive, but also to the Exact Sciences. In astronomi- 
cal calculations, for example, very few of the data rest 
upon the evidence of our own senses, and we compute by 
the aid of a book of logarithms, the accuracy of which, at 
the present day, no one thinks of verifying by independent 
calculation. 

Testimony and Authority ought to be sharply distin- 
guished from each other, though they are often loosely used 
as synonymous. Properly speaking, we accept Testimony 
as to matters of fact, and yield to Authority in matters of 
opinion. Our confidence in the former depends mainly on 
our opinion of the veracity of our informant ; in tlie latter 
case, we rely chiefly on the soundness of his judgment, the 
accuracy of his habits of reasoning, and the largeness of 
his information. We disbelieve Testimony, we reject Au- 
thority. The reason why these two sources of belief are 
so frequently confounded is, that the provinces of observa- 
tion and of reasoning are not kept sufficiently distinct ; 
the certainty of the Intuition is improperly extended to the 



AND THE CAUSES OF ERROR. 429 

Inference which is drawn from it, and drawn so quickly 
and easily that it is mistaken for a part of the observation 
itself. When Dr. Cullen remarked, with as much truth 
as point, that "there are more false facts than there are 
false theories in the world," he did not mean to impugn 
the general disposition of men to tell the truth. He al- 
luded to what are generally supposed to be facts, and 
which go by that name, but are really nothing but loose 
compounds of matters of opinion with those of observa- 
tion. Probably what he had in mind was the insufficiency 
of the evidence on which the members of his own profes- 
sion, that of Medicine, are often obliged to act. Thus, it 
is said that a patient is in a Consumption ; this, if true, 
would be a fact ; but the only known fact is, that certain 
symptoms were manifested fii'om which it was inferred, 
perhaps wrongly, that the case was one of Consumption. 
Again, it is announced as a fact, that the use of a certain 
medicine cured the disease ; when the truth is, that the 
dose was administered, and the man got well, perhaps in 
spite of the medicine. Men are so prone to confound their 
own crude conjectures with what they have actually seen 
or heard, that very few, except those who have been care- 
ftilly trained to scientific habits of mind, can be trusted to 
report their own observations, until they have undergone 
a severe cross-examination. They do not intend to de- 
ceive others, but they have effectually deceived them- 
selves. The reputed sciences of Phrenology and Animal 
Magnetism rested exclusively, in the opinion of their ad- 
mirers, on a basis of observed facts, and hence were to be 
maintained, in spite of the arguments with which they 
were assailed, because facts are admitted to be a better 
test of tnith than reasoning. But it became evident on 
severe scrutiny, that this basis was made up, for the most 
part, out of what Dr. Cullen calls " false facts." 

On account of this fi-equent confusion of two very dis- 



430 THE SOURCES OF EVIDENCE 

similar things, it is commonly said, and with good reason, 
that before accepting Testimony, we ought to have satis- 
factory proof both of the veracity and the comjpetency of 
the witness. But if people generally could be trusted to 
separate their Inferences from their observations, and to 
report the latter unmixed, it would evidently be enough 
to have assurance only upon the former point. In respect 
only to their quahty or certainty, though not with regard 
to their extent or comprehensiveness, one man's Intuitions 
are as good as another's. The one, indeed, may see more 
than the other, because he knows where to look and what 
to observe. He will therefore have more to report, or, at 
any rate, more that is pertinent and useful. But the Tes- 
timony of the other, as far as it goes, will be equally valid 
and trustworthy, for it is equally a report of what has actu- 
ally been observed, and the Intuitive faculty cannot de- 
ceive. The only doubt, then, which can properly affect 
the reception of Testimony, or the admission of other peo- 
ple's experience as at least of equal value with our own, is 
that whicli regards the disposition of the witness to tell the 
truth. Doubts respecting his competency as an observer 
can be settled by sifting the report itself, better than by 
inquiring into tlie abilities of him who made it. 

The proper distinction to be made is, that the claims of 
Testimony to be accepted depend upon the evidence which 
is offered as to the Veracity of the witness, while those of 
Authority rest upon the proofs which we possess of the 
Competency of the person whose opinions we are invited 
to follow. The rules for forming an estimate either of the 
Veracity of an observer or the Competency of a judge are 
too obvious to need mention here, except in very general 
terms. " In regard to the honesty of a witness," says 
Esser, as translated by Hamilton, " this, though often 
admitting of the highest probability, never admits of abso- 
lute certainty ; for though, in many cases, we may know 



AND THE CAUSES OF ERROR. 431 

enough of tlie general character of the witness to rely with 
perfect confidence on his Veracity, in no case can we look 
into the heart, and observe the influence which motives 
have actually had upon his volitions. We are, however, 
compelled, in many of the most important concerns of our 
existence, to depend on the Testimony, and consequently 
to confide in the sincerity, of others. But, from the moral 
constitution of human nature, we are waiTanted in presum- 
ing on the honesty of a witness ; and this presumption is 
enhanced in proportion as the following circumstances con- 
cur in its confirmation. In the first place, a witness is pre- 
sumed to be veracious in this case, in proportion as his love 
of truth is already established from others. In the second 
place, a witness is to be presumed veracious, in proportion 
as he has fewer and weaker motives to falsify his Testi- 
mony. In the third place, a witness is to be presumed 
veracious, in proportion to the likelihood of contradiction 
which his Testimony would encounter, if he deviated from 
the truth." 

In respect to the Competency of the person to whose 
Authority we are requested to defer, the only important 
principle which needs to be here laid down is contained in 
the old adage, Cuique credenduni est in sud arte, — Tiiist 
each person in his own specialty. Eminence in one depart- 
ment of science, far from being an indication of superior 
power of judgment and reasoning in other departments, 
is often a disqualification for forming a correct opinion in 
them. The mind is prone to carry over the special forms 
and processes which are appropriate to one science into 
others, where they are out of place, and lead only to error. 
To adopt Bacon's expressive metaphor, it imports into a 
new sphere of research the rust and tarnish contracted in 
the workshop wherein it has chiefly labored. A distin- 
guished mathematician, other things being equal, is not so 
competent to form an opinion upon some disputed point in 



432 THE SOURCES OF EVIDENCE 

the moral sciences, as one who is conversant with ques- 
tions of this sort, though he has never gahaed distinction 
in them, and may be ignorant of the first principles of 
Algebra and the Calculus. " The merit of a mathemati- 
cal invention," as Hamilton justly remarks, " consists in 
the amount of thought which it supersedes"; and hence 
it is matter of common remark, that those wlio are most 
capable of making such inventions, and profiting by them, 
are least fitted for reasoning by Induction and Analogy. 
Consequently, " Mathematics afford us no assistance either 
in conquering the difficulties, or in avoiding the dangers, 
which we encounter in the great field of probabilities 
wherein we live and move." 

Hume's celebrated argument against the credibility of 
miracles is a fallacy which results from losing sight of the 
distinction between Testimony and Authority, between 
Veracity and Competency. He argues, that it is contrary 
to all experience that a Law of Nature should be broken, 
but it is not contrary to experience that human testimony 
should be false ; and therefore we ought to believe that 
any amount of Testimony is false, in preference to admit- 
ting the occurrence of a miracle, as this would be a viola- 
tion of Law. We answer, that the miraculous character 
of an event is not a matter of Lituition, but of Liference ; 
hence, it is not to be decided by Testimony, but by Rea- 
soning fi'om the probabilities of the case, the only question 
being whether, in view of all the cncumstances, the Con- 
clusion is competent that the occurrence was supernatural. 
The Testimony relates only to the happening of the event 
considered merely as an external phenomenon ; the ques- 
tion respecting the natm-e of this event, whether it is, or is 
not, a violation of Physical Law, whether it is an eflPect 
of this or that Efficient Cause, cannot be determined by 
Intuition and Testimony, but is a matter for Judgment 
founded on Reasoning, in view of all the circumstances of 



AND THE CAUSES OF ERROR. 433 

the case. If doubtful of our own Competency to form a 
correct opinion on this point, we may defer to the Author- 
ity of another, who is famihar with the kind of Reasoning 
by which such questions are settled. Now we have abun- 
dant evidence from experience, that no event whatever, 
regarded simply as an external phenomenon, can be so 
strange and marvellous that sufficient Testimony will not 
convince us of the reality of its occurrence. To the con- 
temporaries of our Saviour, not even bringing a dead man 
to life would have appeared so incredible as the transmis- 
sion of a written message five thousand miles, without 
error, within a minute of time. Yet this feat has been 
accomplished by the Magnetic Telegraph. Why do we 
decide, tlien, that the raising of Lazarus was, and the 
transmission of intelligence by telegraph is not, a mira- 
cle ? Evidently not by Intuition, but by reasoning from 
the very different circumstances of the two cases. The 
fact,, that the eyes of the blind were opened, or a storm was 
reduced to a calm, or the dead were raised, is established 
by Intuition and Testimony, which have established many 
other facts quite as wonderful ; the cliaracier of this fact, 
whether miraculous or not, is to be settled in a very dif- 
ferent manner. We say, then, that Hume's argument, 
which is based exclusively upon an appeal to experience 
and Testimony, is totally inapplicable to the question re- 
specting the credibility of a miracle. Testimony has noth- 
ing to do with the correct inference of a Conclusion from 
its Premises. 

We can touch only very briefly on the Criticism of re- 
corded Testimony, and of writings in general. As we must 
avail ourselves, in the construction of Science, of the ex- 
perience of former generations, in respect to which the 
Testimony of eye- and ear-witnesses is no longer directly 
accessible, we are obliged to consider the credibiKty of 
tliis Testimony as affected by the channels of transmission 

19 BB 



434 THE SOURCES OF EVIDENCE 

through which it has been passed. There are but two such 
channels, Tradition and Ancient Writings. The former 
of these may be left out of account ; for if the lapse of time 
has been considerable, the probability that the Testimony, 
if transmitted merely by word of mouth, has been mate- 
rially altered or falsified, is so great, that the report can be 
received only with extreme caution. But it has already 
been mentioned, that the invention of the art of writing has 
rendered it possible for the experience of a former genera- 
tion to be handed down, through an indefinite lapse of cen- 
turies, in as perfect a state as that in which it was first 
communicated to those who were the contemporaries of 
the events narrated. This is possible, we say; the ques- 
tion whether it has been actually so transmitted is what we 
have to consider in the Criticism of Ancient Writings. 

When a document purporting to be the recorded Testi- 
mony of certain individuals of a former generation is pre- 
sented to us, we have first to inquire whether it is actually 
the handwriting, or the composition as taken down by dic- 
tation, or a faithful report, made at the time, of the sub- 
stance of the evidence of the individuals whose names it 
bears, or to whom it is attributed. The establishment of 
either of these three points is the proof of what is called 
the Grenuineness of the writing. It is comparatively un- 
important which of the three is proved, as either of them 
gives us assurance that the document is a faithful record 
of the Testimony of the persons whose evidence is to be 
weighed. Thus, even if we were sure that the Testimony 
of the Evangelists was originally written out by their own 
hands, we certainly do not possess their autograph copies ; 
still, the Gospels are Genuine, if we have sufficient evi- 
dence that they are faithful records, made at the time, (or 
correct transcripts of such records,) of what the Evange- 
lists said. 

But a second question must be answered before we can 



AND THE CAUSES OF ERROR. 435 

accept the evidence furnished by the document. We must 
be satisfied, not only that the Testimony is Genuine, — that 
it was actually given by those ft-om whom it pui'ports to 
come, but that it is Authentic, — that this Testimony is 
a true and faithful narrative of what actually happened. 
Proofs of the Genuineness of the writing amount, at the 
utmost, only to bringing the witnesses into court and estab- 
lishing their identity ; proofs of the Authenticity must be 
found by sifting their evidence, and applying to it all the 
tests and means of verification which we possess, in order 
to ascertain whether they are telling the truth. If not 
Genuine, the document is said to be Spurious ; if not 
Authentic, it is false. 

As most of the tests and proofs of the Genuineness and 
Authenticity of a writing are such as readily suggest them- 
selves to the inquirer, it is unnecessary to consider them 
here at any length. Generally, they may be divided pto 
two classes, called respectively the External and the Inter- 
nal Evidences of the point to be proved. The External 
Evidences of Genuineness are to be found either in other 
and admitted writings of the supposed author, or in the 
works of writers who were either his contemporaries, or 
nearly of the same antiquity ; and the evidence is either 
direct, if the disputed ^vriting is therein explicitly attributed 
to hira, or indirect, if these works quote as his production 
passages which are found in the document. This indirect 
testimony has the greater force, for on account of its casual 
or incidental character there is less reason to suspect that it 
has been forged. The External Evidences of the Authen- 
ticity of the writing, considered as a narrative of facts, are 
too numerous to mention. They are found in allusions to 
the same facts, or to incidents obviously connected with 
them, by contemporary authors ; in customs, traditions, and 
institutions, which have come down to later times, and the 
origin of which cannot be accounted for, except on the sup- 



436 THE SOURCES OF EVIDENCE 

position that the reported events actually took place ; in 
coins, medals, and inscriptions, belonging to the same age, 
or one immediately subsequent, and connected by equally 
close relations with the alleged facts ; in the notoriety 
which such incidents must have obtained, the interest which 
must have been felt in them, and the consequent probabil- 
ity that falsifications and forgeries respecting them would 
never have been attempted, or would have been detected 
and disproved at the time. 

Of the Internal Evidence, it has been justly remarked, 
that it is weak to establish either Genuineness or Authen- 
ticity, but powerful to disprove both. As Hamilton remarks, 
" We can easily conceive that an able and learned forger 
may accommodate his fabrications both to all the general 
circumstances of time, place, people, and language under 
which it is supposed to have been written, and even to all 
the particular circumstances of the style, habit of thought, 
personal relations, &c. of the supposed author." On the 
other hand, a single anachronism, well made out, in respect 
either to events, institutions, customs, or even the use of 
language, is as fatal to the document's claim to antiquity, as 
a well-established alibi is to the success of a criminal prose- 
cution. Bentley's Dissertation upon the Epistles of Phala- 
ris might have been limited to pointing out two or three of 
the numerous anachronisms which he detected in them, if 
his only object in writing it had been to prove that these 
alleged Epistles were an impudent forgery. In respect to 
the Authenticity of a narrative, it is to be observed, that 
the credibility of certain facts is one thing, and the proof 
of their actual occurrence is another. For establishing the 
former. Internal Evidence is sufficient ; for the latter, it is 
powerless, being entirely inapplicable. By saying that a 
narrative of certain events bears with it Internal Evidence 
of its truth, we mean only that the events are possible, — 
that they are consistent with each other, — that they liar- 



AND THE CAUSES OF ERROR. 437 

monize with what we know from other sources concerning 
the men of that country and that age, — that they are con- 
formable to the ordinary course of things. All this may be 
true of an avowed fiction. Some of Shakespeare's plays, 
most of Scott's novels, have as much Internal Evidence of 
truth as any testimony given in a court of justice. They 
may have even more ; for it is a common proverb that truth 
is often stranger than fiction. If we disregard all extrane- 
ous circumstances, and look only at the face of the narra- 
tive, Robinson Crusoe appears as true a story as Cook's 
Voyages, and Richardson the novelist is as faithftd an his- 
torian as Hume. 

As the evidence from the several sources that have now 
been mentioned may be of various degrees of strength, and 
as opinion is often drawn in opposite directions by conflict- 
ing testimony, we are naturally led to inquire whether 
there is any measure of probability/, or any means of accu- 
rately estimating the amount of belief which ought to be 
accorded under different circumstances. This brings us at 
once to the Theory of Probabilities, or, as the mathemati- 
cians sometimes call it, the Doctrine of Chances. Only 
the outlines, or first principles, of the subject can be con- 
sidered here, as the details are exclusively mathematical, 
and so do not come within our province. 

It is first to be observed, that, in the calculation ot 
Chances, as in every other department of pure mathe- 
matics, since the reasoning employed is Demonstrative in 
character, the correctness of the results obtained depends 
upon the truth of certain assumptions made in the outset ; 
and the applicability of one of these results to any given 
case, or actual instance, turns upon the answer to the ques- 
tion whether this instance is exactly comprehended within 
the Definition of the Concept upon which the whole calcu- 
lation is based. Thus, in calculating the probability of any 
one out of a given number of events, it is assumed that all 



438 THE SOURCES OF EVIDENCE 

the events considered are equally possible, — that no one 
has any advantage which would render it more likely to 
happen than the others. Practically, this supposition is 
never fulfilled. In illustrating their conclusions, the mathe- 
maticians have shown much ingenuity in selecting cases 
where the chances would seem to be equally balanced ; but 
it is easy to show that they have never entirely succeeded. 
Their favorite case is that of putting a number of balls, 
equal in size, but different in color, into an urn, and then 
considering the probability of a blindfolded person drawing 
one of a certain color after a given number of trials. But 
suppose the number of balls is considerable, that all the 
white ones are first thrown in together, and then all the 
black ones ; in such case, the chance of drawing a black 
ball at the first trial is obviously much greater than that of 
a white one. A dozen other suppositions might be made, 
depending on the size and shape of the urn, and the manner 
of throwing in the balls, any one of which would be fatal to 
a precise agreement of the actual with the calculated result. 
Another favorite case is that of throwing up a half-penny, 
to determine whether it will give head or tail ; but here it 
is assumed that the two sides of the coin just balance each 
other, which, on account of the different imprints that they 
bear, is never the case. Even in the better chosen illus- 
trations, then, the calculated result will be only an approx- 
imation to the truth. In ordinary cases in which the Doc- 
trine of Chances is applied, as in gambHng, it will be but a 
rude approximation ; most of what are called games of 
chance are, at least in some faint degree, games of sldll ; 
and in the long run, though not necessarily in a few trials, 
skill will tell. 

In most cases of the practical application of the Doctrine 
of Chances, the existence of numerous causes of error is 
admitted ; but as we know nothing of the character of these 
causes, and do not see any reason why more of them should 



AND THE CAUSES OF ERROR. 439 

operate on one side than on the other, it is assumed that, in 
the long run, they will compensate each other, so that the 
result will agree with the calculation. But this is only the 
argument ad ignorantiam, the fallacy of which has ah'eady 
been noticed ; because we do not know any reason why there 
should not be as many and as heavy errors on one side as 
on the other, it does not follow that there is no such rea- 
son. It was for a long time supposed, that the arithmetical 
mean of several distinct observations of the same astrono- 
mical phenomenon would afford the nearest approximation 
to a correct result, as there was no known reason why dif- 
ferent observers should not err as much on one side as on 
the other. But it is now known that each observer has a 
constant tendency, distinctly appreciable in amount, to err 
in one direction ; and if allowance is not made for this 
" personal equation," as it is called, the arithmetical mean 
is not the nearest attainable approximation to the truth. 

What is called " the Method of Least Squares " has been 
adopted as a mode of finding the most probable result in 
those cases in which the arithmetical mean is not an applica- 
ble expedient for detennining this probability. This Method 
proceeds upon the assumption that all errors are not equally 
probable, but that small errors are more probable than large 
ones. An easy corollaiy from this assumption is, that the 
most probable conclusion can be obtained by making, not 
the errors themselves, but the sum of the squares of these 
errors, of the smallest possible amount. To borrow an in- 
stance from Dr. Whewell : — Let the observed numbers be 
4, 12, 14 ; and suppose it known that these numbers must 
be erroneous, as they ought to form an arithmetical pro- 
gression. The question is, what arithmetical progression 
do they most probably represent. The following table 
shows that there are three such progressions which approx- 
imate the observed series, and also indicates which one of 
them, according to the Method of Least Squares, is the 
most probable. 



440 



THE SOURCES OF EVIDENCE 



Observed Series 
Ist Progression 
2d « 

3d « 

We here see. 



4, 12, 14 

4, 9, 14 
6, 10, 14 

5, 10, 15 



Errors. 

0, 3, 
2, 2, 

1, 2, 1 



Sums of 
errors. 



Sums of squares 
of errors. 



although the first progression gives the 
least sum of errors, the third shows the least sum of the 
squares of the errors; and therefore, according to this 
Method, the third is the most probable of the three. 

These remarks were necessary in order to obviate the 
inference which too many are inclined to draw, that, be- 
cause the calculations in the Doctrine of Chances are made 
on strict mathematical principles, the calculated probability 
of an event, in any actual application of this Doctrine, 
must therefore be mathematically exact and absolutely 
certain. On the contrary, in any such application of the 
principles, the result is only a rough approximation to the 
truth. 

It is also important to remember, that the application of 
the Theory of Probabilities only shows us what we ought 
to expect, or what, as rational beings, we are bound to be- 
lieve, and does not reveal any Cause or Law that actually 
determines the occurrence. To speak technically, the cal- 
culated probability is subjective, and not objective ; it re- 
veals what may be called a law of thought, but not a law 
of things. " The subject-matter of calculations in the 
Theory of Probabilities," says Professor Donkin, " is quan- 
tity of belief. In every problem, a certain number of hy- 
potheses are presented to the mmd, along with a certain 
quantity of information relating to them ; the question is, — 
In what way ought belief to be distributed among them ? " 
The calculation of the chances does not assume to increase 
this " quantity of information," or to reveal any new data 
on which our judgment ought to be based ; but only how 
we ought to judge and to act on the data that we already 



AND THE CAUSES OF ERROR. 441 

possess. The doctrine does not even assure us that the 
calculated result will be verified at the first trial, or at any 
subsequent trial ; but it only shows us how we ought to 
expect the actual results to be distributed in the course of 
an infinite number of trials. The calculation does not re- 
late merely to future events, the occurrence of which is 
still contingent ; it may be applied also to the past, to de- 
termine the probability that the event did, or did not, take 
place. In cases of the latter sort, it is sufficiently obvious 
that the application of the Theory of Probabilities does not 
in any wise affect the event itself, which is already irrev- 
ocably determined either one way or the other ; but only 
assvimes, in our ignorance of what the actual result has 
been, to determine what we ought to believe respecting it. 

Keeping this distinction in mind, we can explain the 
seeming paradox, that an event should be sure to happen 
at the first trial, though the chances were indefinitely gi'eat 
against its occurrence. Put into an urn any number of 
balls numbered consecutively from one upwards, — say 
1,000. Of course, there are 999 chances to 1 against a 
blindfolded person drawing, at the first trial, the particular 
ball marked with any one of these numbers ; and yet some 
one ball so marked must be drawn. But this is no viola- 
tion of the law regulating what we ought to expect ; for 
we ought not to expect any particular number to come at 
the first trial, though we are certain that some — we know 
not what — number must so come. 

It is assumed in the Doctrine of Chances, that the va- 
rious degrees of belief may be represented by numbers. 
An impossible event, as it has no probability whatever in 
its favor, is appropriately represented by zero. An event 
which is sure to happen, as the expectation of its occur- 
rence is not broken or divided by any chance of failure, 
might be represented by any integral number; its most 
convenient, because the simplest, symbol is unity. Then 

19* 



442 THE SOURCES OF EVIDENCE 

all the degrees of probability between impossibility and 
certainty will be denoted by the fractions that may be in- 
terpolated between and 1. 

The first principle of the Doctrine of Chances is, that 
the probability/ of an uncertain event is represented by the 
number of chances favorable to its occurrence, divided by the 
total number of chances whether favorable or unfavorahle. 
Thus, as a pack contains 62 cards, divided into four equal 
suits, into 12 pictured and 40 plain cards, and into 26 red 
and 26 black cards, the chance of drawing a heart at the 
first trial is -^ or \ ; of a pictured card, l-| or -^-^ ; of a red 
card, II or ^. This last case represents an event which is 
entirely uncertain, the chances being equal for and against 
its occurrence. "We may get rid of the fractional form by 
expressing the probabiHty of an event in that mode which 
is called " the odds " ; that is, we may take the numerator 
to express the chances for, and the difference between the 
numerator and the denominator to signify the chances 
against, the occurrence. This rule is an immediate corol- 
lary from the first principle as just stated, since the numer- 
ator gives the number of favorable chances, and the de- 
nominator the total number of them both favorable and 
unfavorable. Thus, the chance of drawing a pictured card 
is represented fractionally, as above, by -j^g-, or by the odds 
as 3 to 10 ; of a red card, as ||-, or 26 to 26, — even 
chance. 

The improbability of an occurrence is denoted by the 
complement of the fraction which expresses its probability ; 
that is, the odds are reversed. Thus, as there are six faces 
to a die, all of which are supposed to be equally likely to 
come uppermost, the probability of throwing six is |- or 1 
to 5 ; the improbability of it is 1 — ^ = |, or 5 to 1. The 
reason of this rule is obvious ; the improbability of one 
event must be th« sum of the probabilities of all the other 
possible occurrences ; and as the total of all the chances. 



AND THE CAUSES OF ERROR. 443 

which represents what is sure to happen, is unity, the sum 
of the probabilities of all the others is found by subtract- 
ing the probability of this one from unity. Thus, some 
one of the six faces must come uppermost ; this certainty 
is denoted as 1. Then, as the probability of a six is ^, the 
chance of some one out of the other five faces, (in other 
words, the improhahility of a six,) is 1 — 1 = |-. As each 
of the five other faces has a probability of ^, the sum of 
their chances, or the improbabihty of the remaining one, is 
evidently |. 

The probability of a compound event — that is, of two 
independent uncertainties happening conjointly — is ascer- 
tained hy multiplying- the separate chances of the two to- 
g-ether. Thus, the chance of throwing six with one die 
being |^, and of thro^ving the same with another die being 
^, the chance of obtaining sixes at once with the two dice 
is I X I = YQ. This rule, again, is a direct corollary from 
the first principle as already enounced ; for as the number 
of possible throws with two dice is 6 X 6 = 36, (since 
each face of the one might be combined with either of the 
six faces of the other,) and as only one of these is favor- 
able, the odds are evidently as 1 to 35. To take another 
instance : — the chance of drawing a pictured card out of 
a pack being -^, and of a red card, |^, the probability of 
having a red pictured card is ^^ X |- = ^6 °^ "^' ^^ there 
are six red pictured cards out of the 52 in the pack. 

According to this rule, the chance of drawing a red card 
four times in succession, the card being replaced after each 
trial, so that the number in the pack shall always be 52, 
will be I X I X l^ X ^ = ^q, or only 1 to 15. But gam- 
blers often deceive themselves in respect to the application 
of this rule. As it is so unlikely that a red card will turn 
up several times in succession, they imagine that, after it 
has thrice thus turned up, the chance of obtaining a black 
card at the fourth trial is much greater than it was at first. 



444 THE SOURCES OF EVIDENCE 

But it is not so ; if the card drawn is always immediately 
replaced, the probability of drawing a black card after we 
have drawn a red one at three, or even at a thousand, suc- 
cessive trials, is precisely what it was before the first ex- 
periment, — namely, |. The number of cards being always 
the same, 26 red and 26 black, the probability of obtaining 
a red one is always the same, whatever previous experiments 
may have been made with the same pack. The three ex- 
periments already tried have reduced so many uncertainties 
to certainties, — that is, have thrown them out of the cal- 
culation in the Doctrine of Chances, which deals only with 
uncertain events. Before any trial was made, the chance 
of a red card turning up four times in succession was only 
■j^, each of the four results being then uncertain ; after 
three trials, but one event is still an uncertainty, and the 
probability of its occurrence is ^. We see, then, the folly 
of the gambler's expectation that his luck must soon timi, 
because he has had a long series of ill-luck. But all his 
past trials having been reduced to certainties, his chance 
of good fortune is now precisely what it was when he be- 
gan. His only chance of success, after he has had a long 
series of misfortunes, is to stop playing altogether; and this 
is also the best thing he can do, if fortune has smiled upon 
him. 

The development of these principles must be left to the 
mathematician ; but a further caution in respect to the 
application to be made of them by the gambler may be 
borrowed from Buffon. " If two men," he asks, " were to 
determine to play for their whole property, what would be 
the effect of this agreement ? The one would only double 
his fortune, and the other reduce his to naught. What 
proportion is there between the loss and the gain ? The 
same that there is between all and notJdng. Tlie gain of 
the one is bvit a moderate sum ; the loss of the otlier is 
numerically infinite, and morally so great that the labor of 



AND THE CAUSES OF ERROR. 445 

his whole life may not, perhaps, suffice to restore his prop- 
erty." But the fascination of gambling is so gi-eat, and 
the habit of it, when once formed, is so incontrollable, that 
every one who even begins to play may be regarded as 
staking his whole fortune upon the issue, and thus as volun- 
tarily subjecting himself to these tremendous odds. 

The principal intellectual Causes of Error have been al- 
ready indirectly considered, inasmuch as they consist in any 
violation of the rules and methods which have been laid 
down for the attainment of truth. But the moral Causes 
wliich bhnd our perceptions, warp our judgments, and lead 
us to accept illusions in the place of truths, deserve some 
separate notice. Most of these are modifications or conse- 
quences of self-love, or rather of that short-sighted selfish- 
ness which has more regard for present ease and enjoyment, 
however trifling, than for future good, however great, if 
the latter be attainable only by effort and self-denial. Such 
are prejudices, pride, undue desires, precipitancy, and sloth. 
All of these are faults of character rather than of intellect ; 
yet they are more frequent sources of delusion, and more 
formidable obstacles to our mental progress, than can be 
found in the original weakness and limited range of our 
faculties, or in the insufficiency of the aids and incitements 
which nature furnishes for the pursuit of truth. We ap- 
proach the study of a subject, not as prepared to accept any 
conclusions to which our researches might naturally lead, 
but with minds stuffed with preconceived opinions, which 
pride prevents us from relinquishing after they have been 
once avowed, or with a bias in favor of some startling con- 
sequences of the inquiry, the announcement of which may 
feed our vanity or establish our reputation. Pride also 
leads us astray, by inducing us to over-estimate the extent 
and importance of the acquisitions that we have already 
made, or to adopt too easily the conclusion that the investi- 
gation has reached its limit, and that we, already know as 



446 THE SOURCES OF EVIDENCE 

much as is capable of being known. I know of no error 
which is more fatal to progress than the idea that there is 
no progress to be made, — of no opinion which is more det- 
rimental to improvement than the belief that no improve- 
ment is possible. It is true that a low estimate of the ex- 
tent of oiu" knowledge does not amount to the Christian 
virtue of humility in the largest sense. It may be, it fre- 
quently is, accompanied with a very lofty opinion of the 
extent of our powers, or the excellence of our natural en- 
dowments. But a conceit of ability, bad as it is, is not so 
injurious to progress as a conceit of knowledge. The one 
encourages a person to study, by leading him to beheve that 
he can grapple with any subject ; the other disposes him to 
sit down in idleness, under the belief that he has already 
mastered that subject. Seneca says, Multos potuisse ad 
sapientiam pervenire, nisi putassent se pervenisse, — Many 
might have obtained wisdom, if they had not supposed that 
they had already got it. 

Moderation in our personal desires, and that earnestness 
of inquiring purpose which leads not so much to an abne- 
gation as to the entire forgetfulness of self, are more im- 
portant elements of success in the pursuit of truth than is 
commonly supposed. The brilliant results of Dr. Frank- 
lin's scientific career seem attributable, in a gi'eat degree, 
to his generous disregard of his own fame and standing in 
the eyes of the public. A lively curiosity, an eye quick at 
observation, great sagacity in detecting the more occult re- 
lations of facts and bearings of experiments, and a mind of 
incessant and intense activity, were not the only means 
that enabled him to accomphsh so much in science. His 
attention was not diverted from the object of investigation 
by any regard for what the world might think of the im- 
portance of that object, or of his own merit in obtaining it. 
The necessary experiments were instituted, not to convince 
others, but to satisfy himself. The most brilliant results at 



AND THE CAUSES OF ERROR. ^447 

which he arrived were communicated only in private let- 
ters to a few friends, to whom he left the care of publishing 
them or not, as they saw fit. His theories sat loosely upon 
him, and he modified or abandoned them, when further ob- 
servations made it necessary, without dreading the charge 
of inconsistency, and without shame at confessing a mis- 
take. He was never seduced, by the accidental brilliancy 
or novelty of one object of inquiry, to pay more attention 
to it than to another, apparently of a more homely charac- 
ter, but really of equal interest to a philosophical mind. 
He studied the means of remedying smoky chimneys with 
as much ardor and industry as he showed in penetrating 
the secrets of the clouds, and robbing the thunderbolt of its 
terrors. He formed theories of the earth, and projects for 
cleaning and hghting the streets of Philadelphia, with equal 
zeal ; and having communicated the former in a private 
letter to a friend, and urged upon his fellow-citizens the 
adoption of the latter, he dismissed both from his mind, and 
pursued with fresh interest a wholly difierent set of inves- 
tigations. 

The most frequent cause of failure in any pursuit is the 
lack of earnestness. Habit may impart a kind of mechan- 
ical faciHty in the performance of a given task ; but there 
will be little vigor or energy in the work, if the feelings 
be not deeply interested in it, so that the result shall be 
awaited with eager expectation or trembling anxiety. Long- 
continued labor easily degenerates into mere routine ; and 
then, even though the specific object in view should be ob- 
tained, — though a science should be learned or a liveli- 
hood got, — there wUl be no strain of the faculties, and 
consequently no development of them, — no correction of 
errors, and therefore no discipline of mind. This is the 
secret of the great force displayed, and the large results 
that are often accomplished, by those who are opprobri- 
ously termed "men of one idea," — persons who have con- 



448 



THE SOURCES OF EVIDENCE 



m 



centrated their attention upon one object, and who pursue 
it, regardless of everything else, with all the strength and 
the bitterness of fanaticism. Half an hour of strenuous 
exertion is worth a week of mechanical and desultory la- 
bor. Too often we dawdle over the business of Hfe, instead 
of taking it up with eagerness, and prosecuting it to the end 
as a work of love. There is all the difference in the world 
between an active mind and a passive one ; between ear- 
nestly hunting after truth, and only swallowing knowledge 
inertly, as it is poured into the memory by a teacher or a 
book, and just as quickly washed out again. We are made 
what we are, experts or dolts, much more by our acquired 
habits than by success or failure in the attainment of knowl- 
edge. Aim not so much to be learned, as to be able to 
learn ; one truly wise man is worth a hundred erudite ped- 
ants. The study of Logic itself will do little to cultivate 
our power of reasoning, or to improve our habits of thought, 
except indirectly, by the effort which is necessary for the 
mastery of its principles, and by the endeavor to verify or 
correct them in the course of our subsequent researches. 
What we really need to attain is Logical power, and a 
knowledge of the science of Logic is useful so far only 
as it is conducive to such attainment. 

Among the occasions for the use of this power, that to 
which the gravest responsibility is attached is the formation 
of our opinions. Properly speaking, we must aU begin life 
without any opinions which we can call our own by any 
better right than that of passive inheritance or unconscious 
inoculation. We have probably imbibed most of them just 
as we took the measles or the whooping-cough in infancy, 
from accidental contact with others. We are Whig, Dem- 
ocrat, or Republican, conservative or radical, — we go to 
the Episcopal, Presbyterian, or Congregationalist church, — 
simply because parents and friends thought so, or did so, 
formerly. Now, in one respect, this is all right and just as 



AND THE CAUSES OF ERROR. 449 

it should be. It is fortunate, both for ourselves and the 
world, that we begin life with a set of provisional opinions 
already formed, not by us, but for us. This vis inertice of 
opinion, this tendency of the human mind to move in the 
ruts where others have preceded it, is the great conserva- 
tive principle of society, all that keeps us from intellectual 
and social anarchy. Without it, all the wise men who 
have been before us would have hved in vain, and society 
would drift along helplessly, without keel or rudder. If 
we were not willing to accept opinions before we are able 
to form them for ourselves, — ay, and to chng to them 
with the fondness which early association imparts, — half of 
the time we should act at random, and the other half ex- 
travagantly and foohshly. 

But we cannot pass through life merely as docile chil- 
dren ; and our first duty as men — at any rate, as educated 
and thinking men — is to begin the great work of fashion- 
ing our own creeds in politics, religion, philosophy, and so- 
cial economy. When we have attained our majority, we 
have become as accountable for our opinions as for our con- 
duct. A wise man, however, might hesitate before going 
as far as Descartes, who urges us to begin by doubting 
everything ; his advice is, to take up every question, as it 
were, de novo, with a determination not to accept any an- 
swer to it the correctness of which is not made out by evi- 
dence satisfactory to our own minds, and eHcited by our own 
inquiries. A safer course, as it seems to me, is to begin, 
not by discarding all our previous opinions, but by examin- 
ing the foundations on which they rest. There is just as 
much of prejudice and rashness in presuming that they are 
all false, as in beheving, previous to inquiiy, that they are 
all true. Do not ask. Why may it not be otherwise ? but 
rather. Why is it so ? The presumption is in favor of the 
received doctrines in any science, until good reasons are 
made to appear for doubting or denying them. But the 

CO 



450 SOURCES OF EVIDENCE AND CAUSES OF ERROR. 

duty of inquiry, in order to ascertain whether there are 
such reasons, is one which always exists, and which opens 
the largest and fairest field for the exercise and develop- 
ment of our powers of thought. Only by such exercise 
can we hope to perfect our knowledge of the principles of 
Logic, and to make that knowledge of use to ourselves and 
others. " We employ reason," said the Port-Royalist logi- 
cians, " as an instrument for acquiring the sciences, whereas 
we ought to use the sciences as a means of perfecting our 
reason, correctness of judgment and accuracy of thought 
being infinitely more valuable than all the speculative 
knowledge which we can obtain from the best-established 
sciences. Wise men, therefore, ought to engage in the 
study of the sciences only so far as they conduce to this 
end, and to make them only the training-ground, and 
not the field for the regular employment, of their mental 
powers." 



THE END. 



Cambridge : Stereotyped and Printed by Welch, Bigelow, & Co. 



IRBWy'ZS 



LIBRARY OF CONGRESS 



020 207 209 4 



ly 




